x^2-110x+240=0

Solution for x^2-110x+240=0 equation:

x^2-110x+240=0

a = 1; b = -110; c = +240;
Δ = b2-4ac
Δ = -1102-4·1·240
Δ = 11140
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:

$\sqrt{\Delta}=\sqrt{11140}=\sqrt{4*2785}=\sqrt{4}*\sqrt{2785}=2\sqrt{2785}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{2785}}{2*1}=\frac{110-2\sqrt{2785}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{2785}}{2*1}=\frac{110+2\sqrt{2785}}{2}
$