6x^2=18x^2-6x

Solution for 6x^2=18x^2-6x equation:

6x^2=18x^2-6x

We move all terms to the left:

6x^2-(18x^2-6x)=0

We get rid of parentheses

6x^2-18x^2+6x=0

We add all the numbers together, and all the variables

-12x^2+6x=0

a = -12; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-12)·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6}{2*-12}=\frac{-12}{-24}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-12}=\frac{0}{-24}
=0
$