X(x+3)+5(x-3)=12(x+3)(x-3)

Solution for X(x+3)+5(x-3)=12(x+3)(x-3) equation:

X(X+3)+5(X-3)=12(X+3)(X-3)

We move all terms to the left:

X(X+3)+5(X-3)-(12(X+3)(X-3))=0

We use the square of the difference formula

X^2+X(X+3)+5(X-3)+9=0

We multiply parentheses

X^2+X^2+3X+5X-15+9=0

We add all the numbers together, and all the variables

2X^2+8X-6=0

a = 2; b = 8; c = -6;
Δ = b2-4ac
Δ = 82-4·2·(-6)
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*2}=\frac{-8-4\sqrt{7}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*2}=\frac{-8+4\sqrt{7}}{4}
$