x2-60x-90=0

Solution for x2-60x-90=0 equation:

x2-60x-90=0

We add all the numbers together, and all the variables

x^2-60x-90=0

a = 1; b = -60; c = -90;
Δ = b2-4ac
Δ = -602-4·1·(-90)
Δ = 3960
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:

$\sqrt{\Delta}=\sqrt{3960}=\sqrt{36*110}=\sqrt{36}*\sqrt{110}=6\sqrt{110}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-6\sqrt{110}}{2*1}=\frac{60-6\sqrt{110}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+6\sqrt{110}}{2*1}=\frac{60+6\sqrt{110}}{2}
$