Y=-12x^2+150x

Solution for Y=-12x^2+150x equation:

=-12Y^2+150Y

We move all terms to the left:

-(-12Y^2+150Y)=0

We get rid of parentheses

12Y^2-150Y=0

a = 12; b = -150; c = 0;
Δ = b2-4ac
Δ = -1502-4·12·0
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-150}{2*12}=\frac{0}{24}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+150}{2*12}=\frac{300}{24}
=12+1/2
$