x(3x+2)=(x-6)x

Solution for x(3x+2)=(x-6)x equation:

x(3x+2)=(x-6)x

We move all terms to the left:

x(3x+2)-((x-6)x)=0

We multiply parentheses

3x^2+2x-((x-6)x)=0


We calculate terms in parentheses: -((x-6)x), so:

(x-6)x

We multiply parentheses

x^2-6x

Back to the equation:

-(x^2-6x)


We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+8x=0

a = 2; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·2·0
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*2}=\frac{-16}{4}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*2}=\frac{0}{4}
=0
$