3x(24+x)=180

Solution for 3x(24+x)=180 equation:

3x(24+x)=180

We move all terms to the left:

3x(24+x)-(180)=0

We add all the numbers together, and all the variables

3x(x+24)-180=0

We multiply parentheses

3x^2+72x-180=0

a = 3; b = 72; c = -180;
Δ = b2-4ac
Δ = 722-4·3·(-180)
Δ = 7344
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:

$\sqrt{\Delta}=\sqrt{7344}=\sqrt{144*51}=\sqrt{144}*\sqrt{51}=12\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-12\sqrt{51}}{2*3}=\frac{-72-12\sqrt{51}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+12\sqrt{51}}{2*3}=\frac{-72+12\sqrt{51}}{6}
$