F(x)=4x2-3x-25

Solution for F(x)=4x2-3x-25 equation:

(F)=4F^2-3F-25

We move all terms to the left:

(F)-(4F^2-3F-25)=0

We get rid of parentheses

-4F^2+F+3F+25=0

We add all the numbers together, and all the variables

-4F^2+4F+25=0

a = -4; b = 4; c = +25;
Δ = b2-4ac
Δ = 42-4·(-4)·25
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{26}}{2*-4}=\frac{-4-4\sqrt{26}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{26}}{2*-4}=\frac{-4+4\sqrt{26}}{-8}
$