x^2+108=3x(x+2)

Solution for x^2+108=3x(x+2) equation:

x^2+108=3x(x+2)

We move all terms to the left:

x^2+108-(3x(x+2))=0


We calculate terms in parentheses: -(3x(x+2)), so:

3x(x+2)

We multiply parentheses

3x^2+6x

Back to the equation:

-(3x^2+6x)


We get rid of parentheses

x^2-3x^2-6x+108=0

We add all the numbers together, and all the variables

-2x^2-6x+108=0

a = -2; b = -6; c = +108;
Δ = b2-4ac
Δ = -62-4·(-2)·108
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-30}{2*-2}=\frac{-24}{-4}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+30}{2*-2}=\frac{36}{-4}
=-9
$