48+3x^2=180

Solution for 48+3x^2=180 equation:

48+3x^2=180

We move all terms to the left:

48+3x^2-(180)=0

We add all the numbers together, and all the variables

3x^2-132=0

a = 3; b = 0; c = -132;
Δ = b2-4ac
Δ = 02-4·3·(-132)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{11}}{2*3}=\frac{0-12\sqrt{11}}{6}
=-\frac{12\sqrt{11}}{6}
=-2\sqrt{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{11}}{2*3}=\frac{0+12\sqrt{11}}{6}
=\frac{12\sqrt{11}}{6}
=2\sqrt{11}
$