6x+15=3x(2x+6)

Solution for 6x+15=3x(2x+6) equation:

6x+15=3x(2x+6)

We move all terms to the left:

6x+15-(3x(2x+6))=0


We calculate terms in parentheses: -(3x(2x+6)), so:

3x(2x+6)

We multiply parentheses

6x^2+18x

Back to the equation:

-(6x^2+18x)


We get rid of parentheses

-6x^2+6x-18x+15=0

We add all the numbers together, and all the variables

-6x^2-12x+15=0

a = -6; b = -12; c = +15;
Δ = b2-4ac
Δ = -122-4·(-6)·15
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-6\sqrt{14}}{2*-6}=\frac{12-6\sqrt{14}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+6\sqrt{14}}{2*-6}=\frac{12+6\sqrt{14}}{-12}
$