3x-6x^2=2x^2-3x

Solution for 3x-6x^2=2x^2-3x equation:

3x-6x^2=2x^2-3x

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-8x^2+6x=0

a = -8; b = 6; c = 0;
Δ = b2-4ac
Δ = 62-4·(-8)·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*-8}=\frac{-12}{-16}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6}{2*-8}=\frac{0}{-16}
=0
$