x^2-15x-75=0

Solution for x^2-15x-75=0 equation:

x^2-15x-75=0

a = 1; b = -15; c = -75;
Δ = b2-4ac
Δ = -152-4·1·(-75)
Δ = 525
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:

$\sqrt{\Delta}=\sqrt{525}=\sqrt{25*21}=\sqrt{25}*\sqrt{21}=5\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{21}}{2*1}=\frac{15-5\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{21}}{2*1}=\frac{15+5\sqrt{21}}{2}
$