Y=-x2+10x+75

Solution for Y=-x2+10x+75 equation:

=-Y2+10Y+75

We move all terms to the left:

-(-Y2+10Y+75)=0

We add all the numbers together, and all the variables

-(-1Y^2+10Y+75)=0

We get rid of parentheses

1Y^2-10Y-75=0

We add all the numbers together, and all the variables

Y^2-10Y-75=0

a = 1; b = -10; c = -75;
Δ = b2-4ac
Δ = -102-4·1·(-75)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-20}{2*1}=\frac{-10}{2}
=-5
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+20}{2*1}=\frac{30}{2}
=15
$