X^2+18x=3(48+6x)

Solution for X^2+18x=3(48+6x) equation:

X^2+18X=3(48+6X)

We move all terms to the left:

X^2+18X-(3(48+6X))=0

We add all the numbers together, and all the variables

X^2+18X-(3(6X+48))=0


We calculate terms in parentheses: -(3(6X+48)), so:

3(6X+48)

We multiply parentheses

18X+144

Back to the equation:

-(18X+144)


We get rid of parentheses

X^2+18X-18X-144=0

We add all the numbers together, and all the variables

X^2-144=0

a = 1; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·1·(-144)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24}{2*1}=\frac{-24}{2}
=-12
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24}{2*1}=\frac{24}{2}
=12
$