2x^2-2x=15x-30

Solution for 2x^2-2x=15x-30 equation:

2x^2-2x=15x-30

We move all terms to the left:

2x^2-2x-(15x-30)=0

We get rid of parentheses

2x^2-2x-15x+30=0

We add all the numbers together, and all the variables

2x^2-17x+30=0

a = 2; b = -17; c = +30;
Δ = b2-4ac
Δ = -172-4·2·30
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-7}{2*2}=\frac{10}{4}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+7}{2*2}=\frac{24}{4}
=6
$