F(x)=6x^2+7x-8

Solution for F(x)=6x^2+7x-8 equation:

(F)=6F^2+7F-8

We move all terms to the left:

(F)-(6F^2+7F-8)=0

We get rid of parentheses

-6F^2+F-7F+8=0

We add all the numbers together, and all the variables

-6F^2-6F+8=0

a = -6; b = -6; c = +8;
Δ = b2-4ac
Δ = -62-4·(-6)·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{-(-6)-2\sqrt{57}}{2*-6}=\frac{6-2\sqrt{57}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{57}}{2*-6}=\frac{6+2\sqrt{57}}{-12}
$