F(x)=3x^2-5x-20

Solution for F(x)=3x^2-5x-20 equation:

(F)=3F^2-5F-20

We move all terms to the left:

(F)-(3F^2-5F-20)=0

We get rid of parentheses

-3F^2+F+5F+20=0

We add all the numbers together, and all the variables

-3F^2+6F+20=0

a = -3; b = 6; c = +20;
Δ = b2-4ac
Δ = 62-4·(-3)·20
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*-3}=\frac{-6-2\sqrt{69}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*-3}=\frac{-6+2\sqrt{69}}{-6}
$