10x^2-15x-72=0

Solution for 10x^2-15x-72=0 equation:

10x^2-15x-72=0

a = 10; b = -15; c = -72;
Δ = b2-4ac
Δ = -152-4·10·(-72)
Δ = 3105
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:

$\sqrt{\Delta}=\sqrt{3105}=\sqrt{9*345}=\sqrt{9}*\sqrt{345}=3\sqrt{345}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{345}}{2*10}=\frac{15-3\sqrt{345}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{345}}{2*10}=\frac{15+3\sqrt{345}}{20}
$