4(x^2-36x-72=0)

Solution for 4(x^2-36x-72=0) equation:

4(x^2-36x-72=0)

We move all terms to the left:

4(x^2-36x-72-(0))=0

We multiply parentheses

4x^2-144x-288+0=0

We add all the numbers together, and all the variables

4x^2-144x-288=0

a = 4; b = -144; c = -288;
Δ = b2-4ac
Δ = -1442-4·4·(-288)
Δ = 25344
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:

$\sqrt{\Delta}=\sqrt{25344}=\sqrt{2304*11}=\sqrt{2304}*\sqrt{11}=48\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-48\sqrt{11}}{2*4}=\frac{144-48\sqrt{11}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+48\sqrt{11}}{2*4}=\frac{144+48\sqrt{11}}{8}
$