15x^2-72x-16=0

Solution for 15x^2-72x-16=0 equation:

15x^2-72x-16=0

a = 15; b = -72; c = -16;
Δ = b2-4ac
Δ = -722-4·15·(-16)
Δ = 6144
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:

$\sqrt{\Delta}=\sqrt{6144}=\sqrt{1024*6}=\sqrt{1024}*\sqrt{6}=32\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-32\sqrt{6}}{2*15}=\frac{72-32\sqrt{6}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+32\sqrt{6}}{2*15}=\frac{72+32\sqrt{6}}{30}
$