2x^2+4x+24=180

Solution for 2x^2+4x+24=180 equation:

2x^2+4x+24=180

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x^2+4x-156=0

a = 2; b = 4; c = -156;
Δ = b2-4ac
Δ = 42-4·2·(-156)
Δ = 1264
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:

$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{79}}{2*2}=\frac{-4-4\sqrt{79}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{79}}{2*2}=\frac{-4+4\sqrt{79}}{4}
$