x^2-110x+1500=0

Solution for x^2-110x+1500=0 equation:

x^2-110x+1500=0

a = 1; b = -110; c = +1500;
Δ = b2-4ac
Δ = -1102-4·1·1500
Δ = 6100
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:

$\sqrt{\Delta}=\sqrt{6100}=\sqrt{100*61}=\sqrt{100}*\sqrt{61}=10\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-10\sqrt{61}}{2*1}=\frac{110-10\sqrt{61}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+10\sqrt{61}}{2*1}=\frac{110+10\sqrt{61}}{2}
$