F(x)=20x^2-45x-15

Solution for F(x)=20x^2-45x-15 equation:

(F)=20F^2-45F-15

We move all terms to the left:

(F)-(20F^2-45F-15)=0

We get rid of parentheses

-20F^2+F+45F+15=0

We add all the numbers together, and all the variables

-20F^2+46F+15=0

a = -20; b = 46; c = +15;
Δ = b2-4ac
Δ = 462-4·(-20)·15
Δ = 3316
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3316}=\sqrt{4*829}=\sqrt{4}*\sqrt{829}=2\sqrt{829}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{829}}{2*-20}=\frac{-46-2\sqrt{829}}{-40}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{829}}{2*-20}=\frac{-46+2\sqrt{829}}{-40}
$