Y=0.1x^2-1.5x+5

Solution for Y=0.1x^2-1.5x+5 equation:

=0.1Y^2-1.5Y+5

We move all terms to the left:

-(0.1Y^2-1.5Y+5)=0

We get rid of parentheses

-0.1Y^2+1.5Y-5=0

a = -0.1; b = 1.5; c = -5;
Δ = b2-4ac
Δ = 1.52-4·(-0.1)·(-5)
Δ = 0.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1.5)-\sqrt{0.25}}{2*-0.1}=\frac{-1.5-\sqrt{0.25}}{-0.2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{0.25}}{2*-0.1}=\frac{-1.5+\sqrt{0.25}}{-0.2}
$