5x^2+30=9x^2

Solution for 5x^2+30=9x^2 equation:

5x^2+30=9x^2

We move all terms to the left:

5x^2+30-(9x^2)=0

We add all the numbers together, and all the variables

-4x^2+30=0

a = -4; b = 0; c = +30;
Δ = b2-4ac
Δ = 02-4·(-4)·30
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{30}}{2*-4}=\frac{0-4\sqrt{30}}{-8}
=-\frac{4\sqrt{30}}{-8}
=-\frac{\sqrt{30}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{30}}{2*-4}=\frac{0+4\sqrt{30}}{-8}
=\frac{4\sqrt{30}}{-8}
=\frac{\sqrt{30}}{-2}
$