48x^2=33000

Solution for 48x^2=33000 equation:

48x^2=33000

We move all terms to the left:

48x^2-(33000)=0

a = 48; b = 0; c = -33000;
Δ = b2-4ac
Δ = 02-4·48·(-33000)
Δ = 6336000
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:

$\sqrt{\Delta}=\sqrt{6336000}=\sqrt{57600*110}=\sqrt{57600}*\sqrt{110}=240\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-240\sqrt{110}}{2*48}=\frac{0-240\sqrt{110}}{96}
=-\frac{240\sqrt{110}}{96}
=-\frac{5\sqrt{110}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+240\sqrt{110}}{2*48}=\frac{0+240\sqrt{110}}{96}
=\frac{240\sqrt{110}}{96}
=\frac{5\sqrt{110}}{2}
$