Respuesta :
for
ax²+bx+c=0
[tex]x= \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
so first solve for ax²+bx+c=0 form
2x²=8x-3
minus 8x anda dd 3 both sides
2x²-8x+3=0
a=2
b=-8
c=3
[tex]x= \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
[tex]x= \frac{-(-8)+/- \sqrt{(-8)^2-4(2)(3)} }{2(2)} [/tex]
[tex]x= \frac{8+/- \sqrt{64-24} }{4} [/tex]
[tex]x= \frac{8+/- \sqrt{40} }{4} [/tex]
[tex]x= \frac{8+/- 2\sqrt{10} }{4} [/tex]
[tex]x= \frac{4+/- \sqrt{10} }{2} [/tex]
[tex]x= \frac{4+ \sqrt{10} }{2} [/tex] and [tex]x= \frac{4- \sqrt{10} }{2} [/tex]
ax²+bx+c=0
[tex]x= \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
so first solve for ax²+bx+c=0 form
2x²=8x-3
minus 8x anda dd 3 both sides
2x²-8x+3=0
a=2
b=-8
c=3
[tex]x= \frac{-b+/- \sqrt{b^2-4ac} }{2a} [/tex]
[tex]x= \frac{-(-8)+/- \sqrt{(-8)^2-4(2)(3)} }{2(2)} [/tex]
[tex]x= \frac{8+/- \sqrt{64-24} }{4} [/tex]
[tex]x= \frac{8+/- \sqrt{40} }{4} [/tex]
[tex]x= \frac{8+/- 2\sqrt{10} }{4} [/tex]
[tex]x= \frac{4+/- \sqrt{10} }{2} [/tex]
[tex]x= \frac{4+ \sqrt{10} }{2} [/tex] and [tex]x= \frac{4- \sqrt{10} }{2} [/tex]
The solutions of the given quadratic equation by quadratic formula method are [tex]2 + \frac{1}{2} \sqrt{10}[/tex] and [tex]2-\frac{1}{2} \sqrt{10}[/tex].
What are solutions of a equation?
A solution is an assignment of values to the unknown variables that makes the equality in the equation true. In other words, a solution is a value or a collection of values (one for each unknown) such that, when substituted for the unknowns, the equation becomes an equality.
What is quadratic formula?
A formula that gives the solutions of the general quadratic equation ax2 + bx + c = 0 and that is usually written in the form
[tex]x = \frac{-b\pm \sqrt{b^{2}-4ac } }{2a}[/tex].
According to the given question.
We have a quadratic equation [tex]2x^{2} = 8x -3[/tex].
The above quadratic equation can be written as [tex]2x^{2} -8x + 3 = 0[/tex].
Therrfore, the solution of the given quadratic equation by the quadratic formula method is given by
[tex]x= \frac{8\pm \sqrt{(8)^{2} -4(2)(3)} }{2(2)}[/tex]
[tex]\implies x = \frac{8 \pm \sqrt{64-24} }{4}[/tex]
[tex]\implies x = \frac{8\pm \sqrt{40} }{4}[/tex]
[tex]\implies x = \frac{8\pm 2\sqrt{10} }{4}[/tex]
[tex]\implies x = 2 + \frac{1}{2} \sqrt{10}[/tex] or [tex]2-\frac{1}{2} \sqrt{10}[/tex]
Hence, the solutions of the given quadratic equation by quadratic formula method are [tex]2 + \frac{1}{2} \sqrt{10}[/tex] and [tex]2-\frac{1}{2} \sqrt{10}[/tex].
Find out more information about solutions of quadratic equation by formula method here:
https://brainly.com/question/2771196
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