6x+12=3x(x-10)

Solution for 6x+12=3x(x-10) equation:

6x+12=3x(x-10)

We move all terms to the left:

6x+12-(3x(x-10))=0


We calculate terms in parentheses: -(3x(x-10)), so:

3x(x-10)

We multiply parentheses

3x^2-30x

Back to the equation:

-(3x^2-30x)


We get rid of parentheses

-3x^2+6x+30x+12=0

We add all the numbers together, and all the variables

-3x^2+36x+12=0

a = -3; b = 36; c = +12;
Δ = b2-4ac
Δ = 362-4·(-3)·12
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-12\sqrt{10}}{2*-3}=\frac{-36-12\sqrt{10}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+12\sqrt{10}}{2*-3}=\frac{-36+12\sqrt{10}}{-6}
$