F(x)=5x^2+6x-12

Solution for F(x)=5x^2+6x-12 equation:

(F)=5F^2+6F-12

We move all terms to the left:

(F)-(5F^2+6F-12)=0

We get rid of parentheses

-5F^2+F-6F+12=0

We add all the numbers together, and all the variables

-5F^2-5F+12=0

a = -5; b = -5; c = +12;
Δ = b2-4ac
Δ = -52-4·(-5)·12
Δ = 265
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{265}}{2*-5}=\frac{5-\sqrt{265}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{265}}{2*-5}=\frac{5+\sqrt{265}}{-10}
$