(x-110)x=40

Solution for (x-110)x=40 equation:

(x-110)x=40

We move all terms to the left:

(x-110)x-(40)=0

We multiply parentheses

x^2-110x-40=0

a = 1; b = -110; c = -40;
Δ = b2-4ac
Δ = -1102-4·1·(-40)
Δ = 12260
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:

$\sqrt{\Delta}=\sqrt{12260}=\sqrt{4*3065}=\sqrt{4}*\sqrt{3065}=2\sqrt{3065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{3065}}{2*1}=\frac{110-2\sqrt{3065}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{3065}}{2*1}=\frac{110+2\sqrt{3065}}{2}
$