10x^2-23x=-23x+90

Solution for 10x^2-23x=-23x+90 equation:

10x^2-23x=-23x+90

We move all terms to the left:

10x^2-23x-(-23x+90)=0

We get rid of parentheses

10x^2-23x+23x-90=0

We add all the numbers together, and all the variables

10x^2-90=0

a = 10; b = 0; c = -90;
Δ = b2-4ac
Δ = 02-4·10·(-90)
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-60}{2*10}=\frac{-60}{20}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+60}{2*10}=\frac{60}{20}
=3
$