Y=0.1x^2-2x-12

Solution for Y=0.1x^2-2x-12 equation:

=0.1Y^2-2Y-12

We move all terms to the left:

-(0.1Y^2-2Y-12)=0

We get rid of parentheses

-0.1Y^2+2Y+12=0

a = -0.1; b = 2; c = +12;
Δ = b2-4ac
Δ = 22-4·(-0.1)·12
Δ = 8.8
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{-(2)-\sqrt{8.8}}{2*-0.1}=\frac{-2-\sqrt{8.8}}{-0.2}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+\sqrt{8.8}}{2*-0.1}=\frac{-2+\sqrt{8.8}}{-0.2}
$