Answer:
[tex]\displaystyle x_1=\frac{7+ \sqrt{85}}{6}\approx 2.70\\\displaystyle x_2=\frac{7- \sqrt{85}}{6}\approx -0.37[/tex]
Step-by-step explanation:
Quadratic Formula
Given the second-degree equation:
[tex]ax^2+bx+c=0[/tex]
The solutions of the equation can be obtained by applying the formula:
[tex]\displaystyle x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
The equation to solve is:
[tex]3x^2-7x-3=0[/tex]
Which means the values of the coefficients are: a=3, b=-7, c=-3. Substituting the values in the formula:
[tex]\displaystyle x=\frac{-(-7)\pm \sqrt{(-7)^2-4(3)(-3)}}{2(3)}[/tex]
[tex]\displaystyle x=\frac{7\pm \sqrt{49+36}}{6}[/tex]
[tex]\displaystyle x=\frac{7\pm \sqrt{85}}{6}[/tex]
There are two real solutions for this equation:
[tex]\displaystyle x_1=\frac{7+ \sqrt{85}}{6}[/tex]
[tex]\displaystyle x_2=\frac{7- \sqrt{85}}{6}[/tex]
The approximate values of both roots are:
[tex]x_1\approx 2.70[/tex]
[tex]x_2\approx -0.37[/tex]
