Y=-0.125x^2+1.84x+6

Solution for Y=-0.125x^2+1.84x+6 equation:

=-0.125Y^2+1.84Y+6

We move all terms to the left:

-(-0.125Y^2+1.84Y+6)=0

We get rid of parentheses

0.125Y^2-1.84Y-6=0

a = 0.125; b = -1.84; c = -6;
Δ = b2-4ac
Δ = -1.842-4·0.125·(-6)
Δ = 6.3856
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{-(-1.84)-\sqrt{6.3856}}{2*0.125}=\frac{1.84-\sqrt{6.3856}}{0.25}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.84)+\sqrt{6.3856}}{2*0.125}=\frac{1.84+\sqrt{6.3856}}{0.25}
$