Y=-5x^2+150x+5

Solution for Y=-5x^2+150x+5 equation:

=-5Y^2+150Y+5

We move all terms to the left:

-(-5Y^2+150Y+5)=0

We get rid of parentheses

5Y^2-150Y-5=0

a = 5; b = -150; c = -5;
Δ = b2-4ac
Δ = -1502-4·5·(-5)
Δ = 22600
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:

$\sqrt{\Delta}=\sqrt{22600}=\sqrt{100*226}=\sqrt{100}*\sqrt{226}=10\sqrt{226}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-10\sqrt{226}}{2*5}=\frac{150-10\sqrt{226}}{10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+10\sqrt{226}}{2*5}=\frac{150+10\sqrt{226}}{10}
$