F(1)=4x2-3x-25

Solution for F(1)=4x2-3x-25 equation:

(1)=4F^2-3F-25

We move all terms to the left:

(1)-(4F^2-3F-25)=0

We get rid of parentheses

-4F^2+3F+25+1=0

We add all the numbers together, and all the variables

-4F^2+3F+26=0

a = -4; b = 3; c = +26;
Δ = b2-4ac
Δ = 32-4·(-4)·26
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5\sqrt{17}}{2*-4}=\frac{-3-5\sqrt{17}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5\sqrt{17}}{2*-4}=\frac{-3+5\sqrt{17}}{-8}
$