4x^2-23=-5x^2+13

Solution for 4x^2-23=-5x^2+13 equation:

4x^2-23=-5x^2+13

We move all terms to the left:

4x^2-23-(-5x^2+13)=0

We get rid of parentheses

4x^2+5x^2-13-23=0

We add all the numbers together, and all the variables

9x^2-36=0

a = 9; b = 0; c = -36;
Δ = b2-4ac
Δ = 02-4·9·(-36)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*9}=\frac{-36}{18}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*9}=\frac{36}{18}
=2
$