Y=-0.05x^2+5x-105

Solution for Y=-0.05x^2+5x-105 equation:

=-0.05Y^2+5Y-105

We move all terms to the left:

-(-0.05Y^2+5Y-105)=0

We get rid of parentheses

0.05Y^2-5Y+105=0

a = 0.05; b = -5; c = +105;
Δ = b2-4ac
Δ = -52-4·0.05·105
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-2}{2*0.05}=\frac{3}{0.1}
=30
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+2}{2*0.05}=\frac{7}{0.1}
=70
$