F(x)=6x^2+4x-7

Solution for F(x)=6x^2+4x-7 equation:

(F)=6F^2+4F-7

We move all terms to the left:

(F)-(6F^2+4F-7)=0

We get rid of parentheses

-6F^2+F-4F+7=0

We add all the numbers together, and all the variables

-6F^2-3F+7=0

a = -6; b = -3; c = +7;
Δ = b2-4ac
Δ = -32-4·(-6)·7
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{177}}{2*-6}=\frac{3-\sqrt{177}}{-12}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{177}}{2*-6}=\frac{3+\sqrt{177}}{-12}
$