48-2x^2=9x^2-4

Solution for 48-2x^2=9x^2-4 equation:

48-2x^2=9x^2-4

We move all terms to the left:

48-2x^2-(9x^2-4)=0

We get rid of parentheses

-2x^2-9x^2+4+48=0

We add all the numbers together, and all the variables

-11x^2+52=0

a = -11; b = 0; c = +52;
Δ = b2-4ac
Δ = 02-4·(-11)·52
Δ = 2288
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:

$\sqrt{\Delta}=\sqrt{2288}=\sqrt{16*143}=\sqrt{16}*\sqrt{143}=4\sqrt{143}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{143}}{2*-11}=\frac{0-4\sqrt{143}}{-22}
=-\frac{4\sqrt{143}}{-22}
=-\frac{2\sqrt{143}}{-11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{143}}{2*-11}=\frac{0+4\sqrt{143}}{-22}
=\frac{4\sqrt{143}}{-22}
=\frac{2\sqrt{143}}{-11}
$