24x^2+180x+72=0

Solution for 24x^2+180x+72=0 equation:

24x^2+180x+72=0

a = 24; b = 180; c = +72;
Δ = b2-4ac
Δ = 1802-4·24·72
Δ = 25488
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:

$\sqrt{\Delta}=\sqrt{25488}=\sqrt{144*177}=\sqrt{144}*\sqrt{177}=12\sqrt{177}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-12\sqrt{177}}{2*24}=\frac{-180-12\sqrt{177}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+12\sqrt{177}}{2*24}=\frac{-180+12\sqrt{177}}{48}
$