3x^2-23x=-2x^2-9x-8

Solution for 3x^2-23x=-2x^2-9x-8 equation:

3x^2-23x=-2x^2-9x-8

We move all terms to the left:

3x^2-23x-(-2x^2-9x-8)=0

We get rid of parentheses

3x^2+2x^2+9x-23x+8=0

We add all the numbers together, and all the variables

5x^2-14x+8=0

a = 5; b = -14; c = +8;
Δ = b2-4ac
Δ = -142-4·5·8
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6}{2*5}=\frac{8}{10}
=4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6}{2*5}=\frac{20}{10}
=2
$