480*(0.37-x^2)=180x^2

Solution for 480*(0.37-x^2)=180x^2 equation:

480(0.37-x^2)=180x^2

We move all terms to the left:

480(0.37-x^2)-(180x^2)=0

We add all the numbers together, and all the variables

-180x^2+480(0.37-x^2)=0

We multiply parentheses

-180x^2-480x^2+177.6=0

We add all the numbers together, and all the variables

-660x^2+177.6=0

a = -660; b = 0; c = +177.6;
Δ = b2-4ac
Δ = 02-4·(-660)·177.6
Δ = 468864
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:

$\sqrt{\Delta}=\sqrt{468864}=\sqrt{576*814}=\sqrt{576}*\sqrt{814}=24\sqrt{814}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{814}}{2*-660}=\frac{0-24\sqrt{814}}{-1320}
=-\frac{24\sqrt{814}}{-1320}
=-\frac{\sqrt{814}}{-55}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{814}}{2*-660}=\frac{0+24\sqrt{814}}{-1320}
=\frac{24\sqrt{814}}{-1320}
=\frac{\sqrt{814}}{-55}
$