F(x)=3x2+5x+-6

Solution for F(x)=3x2+5x+-6 equation:

(F)=3F^2+5F+-6

We move all terms to the left:

(F)-(3F^2+5F+-6)=0

We use the square of the difference formula

F-(3F^2+5F-6)=0

We get rid of parentheses

-3F^2+F-5F+6=0

We add all the numbers together, and all the variables

-3F^2-4F+6=0

a = -3; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-3)·6
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{22}}{2*-3}=\frac{4-2\sqrt{22}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{22}}{2*-3}=\frac{4+2\sqrt{22}}{-6}
$