12x=8x(x+20)

Solution for 12x=8x(x+20) equation:

12x=8x(x+20)

We move all terms to the left:

12x-(8x(x+20))=0


We calculate terms in parentheses: -(8x(x+20)), so:

8x(x+20)

We multiply parentheses

8x^2+160x

Back to the equation:

-(8x^2+160x)


We get rid of parentheses

-8x^2+12x-160x=0

We add all the numbers together, and all the variables

-8x^2-148x=0

a = -8; b = -148; c = 0;
Δ = b2-4ac
Δ = -1482-4·(-8)·0
Δ = 21904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21904}=148$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-148)-148}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-148)+148}{2*-8}=\frac{296}{-16}
=-18+1/2
$