Y=-1.5x^2+48x+10

Solution for Y=-1.5x^2+48x+10 equation:

=-1.5Y^2+48Y+10

We move all terms to the left:

-(-1.5Y^2+48Y+10)=0

We get rid of parentheses

1.5Y^2-48Y-10=0

a = 1.5; b = -48; c = -10;
Δ = b2-4ac
Δ = -482-4·1.5·(-10)
Δ = 2364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2364}=\sqrt{4*591}=\sqrt{4}*\sqrt{591}=2\sqrt{591}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{591}}{2*1.5}=\frac{48-2\sqrt{591}}{3}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{591}}{2*1.5}=\frac{48+2\sqrt{591}}{3}
$