5x^2-72x-225=0

Solution for 5x^2-72x-225=0 equation:

5x^2-72x-225=0

a = 5; b = -72; c = -225;
Δ = b2-4ac
Δ = -722-4·5·(-225)
Δ = 9684
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:

$\sqrt{\Delta}=\sqrt{9684}=\sqrt{36*269}=\sqrt{36}*\sqrt{269}=6\sqrt{269}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-6\sqrt{269}}{2*5}=\frac{72-6\sqrt{269}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+6\sqrt{269}}{2*5}=\frac{72+6\sqrt{269}}{10}
$