8x2-36=-x2

Solution for 8x2-36=-x2 equation:

8x^2-36=-x2

We move all terms to the left:

8x^2-36-(-x2)=0

We add all the numbers together, and all the variables

8x^2-(-1x^2)-36=0

We get rid of parentheses

8x^2+1x^2-36=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
$