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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

6x^2-(-2x^2-3x+3)-1x=0

We get rid of parentheses

6x^2+2x^2+3x-1x-3=0

We add all the numbers together, and all the variables

8x^2+2x-3=0

a = 8; b = 2; c = -3;
Δ = b2-4ac
Δ = 22-4·8·(-3)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-10}{2*8}=\frac{-12}{16}
=-3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+10}{2*8}=\frac{8}{16}
=1/2
$