24+(4x2)=180

Solution for 24+(4x2)=180 equation:

24+(4x^2)=180

We move all terms to the left:

24+(4x^2)-(180)=0

We add all the numbers together, and all the variables

4x^2-156=0

a = 4; b = 0; c = -156;
Δ = b2-4ac
Δ = 02-4·4·(-156)
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{39}}{2*4}=\frac{0-8\sqrt{39}}{8}
=-\frac{8\sqrt{39}}{8}
=-\sqrt{39}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{39}}{2*4}=\frac{0+8\sqrt{39}}{8}
=\frac{8\sqrt{39}}{8}
=\sqrt{39}
$