12x=4x(5+x)

Solution for 12x=4x(5+x) equation:

12x=4x(5+x)

We move all terms to the left:

12x-(4x(5+x))=0

We add all the numbers together, and all the variables

12x-(4x(x+5))=0


We calculate terms in parentheses: -(4x(x+5)), so:

4x(x+5)

We multiply parentheses

4x^2+20x

Back to the equation:

-(4x^2+20x)


We get rid of parentheses

-4x^2+12x-20x=0

We add all the numbers together, and all the variables

-4x^2-8x=0

a = -4; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·(-4)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*-4}=\frac{16}{-8}
=-2
$