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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+5x=0

a = -3; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-3)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-3}=\frac{-10}{-6}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-3}=\frac{0}{-6}
=0
$