F(4)=5x^2-4x-7

Solution for F(4)=5x^2-4x-7 equation:

(4)=5F^2-4F-7

We move all terms to the left:

(4)-(5F^2-4F-7)=0

We get rid of parentheses

-5F^2+4F+7+4=0

We add all the numbers together, and all the variables

-5F^2+4F+11=0

a = -5; b = 4; c = +11;
Δ = b2-4ac
Δ = 42-4·(-5)·11
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{59}}{2*-5}=\frac{-4-2\sqrt{59}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{59}}{2*-5}=\frac{-4+2\sqrt{59}}{-10}
$