4-9x^2=x^2-36

Solution for 4-9x^2=x^2-36 equation:

4-9x^2=x^2-36

We move all terms to the left:

4-9x^2-(x^2-36)=0

We get rid of parentheses

-9x^2-x^2+36+4=0

We add all the numbers together, and all the variables

-10x^2+40=0

a = -10; b = 0; c = +40;
Δ = b2-4ac
Δ = 02-4·(-10)·40
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40}{2*-10}=\frac{-40}{-20}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40}{2*-10}=\frac{40}{-20}
=-2
$