110x-x^2=10

Solution for 110x-x^2=10 equation:

110x-x^2=10

We move all terms to the left:

110x-x^2-(10)=0

We add all the numbers together, and all the variables

-1x^2+110x-10=0

a = -1; b = 110; c = -10;
Δ = b2-4ac
Δ = 1102-4·(-1)·(-10)
Δ = 12060
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:

$\sqrt{\Delta}=\sqrt{12060}=\sqrt{36*335}=\sqrt{36}*\sqrt{335}=6\sqrt{335}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-6\sqrt{335}}{2*-1}=\frac{-110-6\sqrt{335}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+6\sqrt{335}}{2*-1}=\frac{-110+6\sqrt{335}}{-2}
$