5x^2+3x-72=0

Solution for 5x^2+3x-72=0 equation:

5x^2+3x-72=0

a = 5; b = 3; c = -72;
Δ = b2-4ac
Δ = 32-4·5·(-72)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{161}}{2*5}=\frac{-3-3\sqrt{161}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{161}}{2*5}=\frac{-3+3\sqrt{161}}{10}
$