Y=0.05x2-4x-38

Solution for Y=0.05x2-4x-38 equation:

=0.05Y^2-4Y-38

We move all terms to the left:

-(0.05Y^2-4Y-38)=0

We get rid of parentheses

-0.05Y^2+4Y+38=0

a = -0.05; b = 4; c = +38;
Δ = b2-4ac
Δ = 42-4·(-0.05)·38
Δ = 23.6
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{-(4)-\sqrt{23.6}}{2*-0.05}=\frac{-4-\sqrt{23.6}}{-0.1}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+\sqrt{23.6}}{2*-0.05}=\frac{-4+\sqrt{23.6}}{-0.1}
$