x^2+12+3x^2+20=180

Solution for x^2+12+3x^2+20=180 equation:

x^2+12+3x^2+20=180

We move all terms to the left:

x^2+12+3x^2+20-(180)=0

We add all the numbers together, and all the variables

4x^2-148=0

a = 4; b = 0; c = -148;
Δ = b2-4ac
Δ = 02-4·4·(-148)
Δ = 2368
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:

$\sqrt{\Delta}=\sqrt{2368}=\sqrt{64*37}=\sqrt{64}*\sqrt{37}=8\sqrt{37}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{37}}{2*4}=\frac{0-8\sqrt{37}}{8}
=-\frac{8\sqrt{37}}{8}
=-\sqrt{37}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{37}}{2*4}=\frac{0+8\sqrt{37}}{8}
=\frac{8\sqrt{37}}{8}
=\sqrt{37}
$