12x-36+2x=-2(2+x)x

Solution for 12x-36+2x=-2(2+x)x equation:

12x-36+2x=-2(2+x)x

We move all terms to the left:

12x-36+2x-(-2(2+x)x)=0

We add all the numbers together, and all the variables

12x+2x-(-2(x+2)x)-36=0

We add all the numbers together, and all the variables

14x-(-2(x+2)x)-36=0


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

-2(x+2)x

We multiply parentheses

-2x^2-4x

Back to the equation:

-(-2x^2-4x)


We get rid of parentheses

2x^2+4x+14x-36=0

We add all the numbers together, and all the variables

2x^2+18x-36=0

a = 2; b = 18; c = -36;
Δ = b2-4ac
Δ = 182-4·2·(-36)
Δ = 612
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:

$\sqrt{\Delta}=\sqrt{612}=\sqrt{36*17}=\sqrt{36}*\sqrt{17}=6\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-6\sqrt{17}}{2*2}=\frac{-18-6\sqrt{17}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+6\sqrt{17}}{2*2}=\frac{-18+6\sqrt{17}}{4}
$