4x^2-32=5x^2+18x

Solution for 4x^2-32=5x^2+18x equation:

4x^2-32=5x^2+18x

We move all terms to the left:

4x^2-32-(5x^2+18x)=0

We get rid of parentheses

4x^2-5x^2-18x-32=0

We add all the numbers together, and all the variables

-1x^2-18x-32=0

a = -1; b = -18; c = -32;
Δ = b2-4ac
Δ = -182-4·(-1)·(-32)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-14}{2*-1}=\frac{4}{-2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+14}{2*-1}=\frac{32}{-2}
=-16
$