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 add all the numbers together, and all the variables

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

We use the square of the difference formula

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-10x^2+36=0

a = -10; b = 0; c = +36;
Δ = b2-4ac
Δ = 02-4·(-10)·36
Δ = 1440
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{10}}{2*-10}=\frac{0-12\sqrt{10}}{-20}
=-\frac{12\sqrt{10}}{-20}
=-\frac{3\sqrt{10}}{-5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{10}}{2*-10}=\frac{0+12\sqrt{10}}{-20}
=\frac{12\sqrt{10}}{-20}
=\frac{3\sqrt{10}}{-5}
$