F8=7x2-4x

Solution for F8=7x2-4x equation:

8=7F^2-4F

We move all terms to the left:

8-(7F^2-4F)=0

We get rid of parentheses

-7F^2+4F+8=0

a = -7; b = 4; c = +8;
Δ = b2-4ac
Δ = 42-4·(-7)·8
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{15}}{2*-7}=\frac{-4-4\sqrt{15}}{-14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{15}}{2*-7}=\frac{-4+4\sqrt{15}}{-14}
$