x^2-180x-6500=0

Solution for x^2-180x-6500=0 equation:

x^2-180x-6500=0

a = 1; b = -180; c = -6500;
Δ = b2-4ac
Δ = -1802-4·1·(-6500)
Δ = 58400
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:

$\sqrt{\Delta}=\sqrt{58400}=\sqrt{400*146}=\sqrt{400}*\sqrt{146}=20\sqrt{146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-20\sqrt{146}}{2*1}=\frac{180-20\sqrt{146}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+20\sqrt{146}}{2*1}=\frac{180+20\sqrt{146}}{2}
$