4x^2-90=5x^2+23x

Solution for 4x^2-90=5x^2+23x equation:

4x^2-90=5x^2+23x

We move all terms to the left:

4x^2-90-(5x^2+23x)=0

We get rid of parentheses

4x^2-5x^2-23x-90=0

We add all the numbers together, and all the variables

-1x^2-23x-90=0

a = -1; b = -23; c = -90;
Δ = b2-4ac
Δ = -232-4·(-1)·(-90)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-13}{2*-1}=\frac{10}{-2}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+13}{2*-1}=\frac{36}{-2}
=-18
$