F(5)=4x2-3x-25

Solution for F(5)=4x2-3x-25 equation:

(5)=4F^2-3F-25

We move all terms to the left:

(5)-(4F^2-3F-25)=0

We get rid of parentheses

-4F^2+3F+25+5=0

We add all the numbers together, and all the variables

-4F^2+3F+30=0

a = -4; b = 3; c = +30;
Δ = b2-4ac
Δ = 32-4·(-4)·30
Δ = 489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{489}}{2*-4}=\frac{-3-\sqrt{489}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{489}}{2*-4}=\frac{-3+\sqrt{489}}{-8}
$