x^2-15x-45=0

Solution for x^2-15x-45=0 equation:

x^2-15x-45=0

a = 1; b = -15; c = -45;
Δ = b2-4ac
Δ = -152-4·1·(-45)
Δ = 405
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:

$\sqrt{\Delta}=\sqrt{405}=\sqrt{81*5}=\sqrt{81}*\sqrt{5}=9\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9\sqrt{5}}{2*1}=\frac{15-9\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9\sqrt{5}}{2*1}=\frac{15+9\sqrt{5}}{2}
$