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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -4; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·(-4)·2
Δ = 57
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{-(-5)-\sqrt{57}}{2*-4}=\frac{5-\sqrt{57}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*-4}=\frac{5+\sqrt{57}}{-8}
$