F(x)=2x^2+5x-6

Solution for F(x)=2x^2+5x-6 equation:

(F)=2F^2+5F-6

We move all terms to the left:

(F)-(2F^2+5F-6)=0

We get rid of parentheses

-2F^2+F-5F+6=0

We add all the numbers together, and all the variables

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

a = -2; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-2)·6
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-2}=\frac{-4}{-4}
=1
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-2}=\frac{12}{-4}
=-3
$