Y=100+10x-x^2

Solution for Y=100+10x-x^2 equation:

=100+10Y-Y^2

We move all terms to the left:

-(100+10Y-Y^2)=0

We get rid of parentheses

Y^2-10Y-100=0

a = 1; b = -10; c = -100;
Δ = b2-4ac
Δ = -102-4·1·(-100)
Δ = 500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{500}=\sqrt{100*5}=\sqrt{100}*\sqrt{5}=10\sqrt{5}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{5}}{2*1}=\frac{10-10\sqrt{5}}{2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{5}}{2*1}=\frac{10+10\sqrt{5}}{2}
$