12-9x=3x(x+10)

Solution for 12-9x=3x(x+10) equation:

12-9x=3x(x+10)

We move all terms to the left:

12-9x-(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^2-9x-30x+12=0

We add all the numbers together, and all the variables

-3x^2-39x+12=0

a = -3; b = -39; c = +12;
Δ = b2-4ac
Δ = -392-4·(-3)·12
Δ = 1665
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:

$\sqrt{\Delta}=\sqrt{1665}=\sqrt{9*185}=\sqrt{9}*\sqrt{185}=3\sqrt{185}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-3\sqrt{185}}{2*-3}=\frac{39-3\sqrt{185}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+3\sqrt{185}}{2*-3}=\frac{39+3\sqrt{185}}{-6}
$