3x-10=2x^2-10x+10

Solution for 3x-10=2x^2-10x+10 equation:

3x-10=2x^2-10x+10

We move all terms to the left:

3x-10-(2x^2-10x+10)=0

We get rid of parentheses

-2x^2+3x+10x-10-10=0

We add all the numbers together, and all the variables

-2x^2+13x-20=0

a = -2; b = 13; c = -20;
Δ = b2-4ac
Δ = 132-4·(-2)·(-20)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-3}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+3}{2*-2}=\frac{-10}{-4}
=2+1/2
$