F(x)=(x+12)(2x-3)

Solution for F(x)=(x+12)(2x-3) equation:

(F)=(F+12)(2F-3)

We move all terms to the left:

(F)-((F+12)(2F-3))=0

We multiply parentheses ..

-((+2F^2-3F+24F-36))+F=0


We calculate terms in parentheses: -((+2F^2-3F+24F-36)), so:

(+2F^2-3F+24F-36)

We get rid of parentheses

2F^2-3F+24F-36

We add all the numbers together, and all the variables

2F^2+21F-36

Back to the equation:

-(2F^2+21F-36)


We add all the numbers together, and all the variables

F-(2F^2+21F-36)=0

We get rid of parentheses

-2F^2+F-21F+36=0

We add all the numbers together, and all the variables

-2F^2-20F+36=0

a = -2; b = -20; c = +36;
Δ = b2-4ac
Δ = -202-4·(-2)·36
Δ = 688
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:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{43}}{2*-2}=\frac{20-4\sqrt{43}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{43}}{2*-2}=\frac{20+4\sqrt{43}}{-4}
$