F(x)=7x^2-x-8

Solution for F(x)=7x^2-x-8 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -7; b = 2; c = +8;
Δ = b2-4ac
Δ = 22-4·(-7)·8
Δ = 228
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:

$\sqrt{\Delta}=\sqrt{228}=\sqrt{4*57}=\sqrt{4}*\sqrt{57}=2\sqrt{57}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{57}}{2*-7}=\frac{-2-2\sqrt{57}}{-14}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{57}}{2*-7}=\frac{-2+2\sqrt{57}}{-14}
$