X^2+12x=2(18+6x)

Solution for X^2+12x=2(18+6x) equation:

X^2+12X=2(18+6X)

We move all terms to the left:

X^2+12X-(2(18+6X))=0

We add all the numbers together, and all the variables

X^2+12X-(2(6X+18))=0


We calculate terms in parentheses: -(2(6X+18)), so:

2(6X+18)

We multiply parentheses

12X+36

Back to the equation:

-(12X+36)


We get rid of parentheses

X^2+12X-12X-36=0

We add all the numbers together, and all the variables

X^2-36=0

a = 1; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·1·(-36)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12}{2*1}=\frac{-12}{2}
=-6
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12}{2*1}=\frac{12}{2}
=6
$