Function intercepts the x-axis where y=0
[tex]f(x) = y = -2x^2 -3x +20 \\
0 = -2x^2-3x+20 \\
[/tex]
We can now calculate the discriminant and find the roots.
[tex]\Delta = (-3)^2 - 4\cdot(-2)\cdot(20) = 169 \\\\
\sqrt\Delta = 13\\\\
x_1 = \frac{-(-3) - 13}{2\cdot(-2)} = \frac{5}{2} \\\\
x_2 = \frac{-(-3) + 13}{2\cdot(-2)} = 4 [/tex]
