4x^2+24x+144=256

Solution for 4x^2+24x+144=256 equation:

4x^2+24x+144=256

We move all terms to the left:

4x^2+24x+144-(256)=0

We add all the numbers together, and all the variables

4x^2+24x-112=0

a = 4; b = 24; c = -112;
Δ = b2-4ac
Δ = 242-4·4·(-112)
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{-(24)-8\sqrt{37}}{2*4}=\frac{-24-8\sqrt{37}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+8\sqrt{37}}{2*4}=\frac{-24+8\sqrt{37}}{8}
$