Y=5t^2+40t-75

Solution for Y=5t^2+40t-75 equation:

=5Y^2+40Y-75

We move all terms to the left:

-(5Y^2+40Y-75)=0

We get rid of parentheses

-5Y^2-40Y+75=0

a = -5; b = -40; c = +75;
Δ = b2-4ac
Δ = -402-4·(-5)·75
Δ = 3100
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:

$\sqrt{\Delta}=\sqrt{3100}=\sqrt{100*31}=\sqrt{100}*\sqrt{31}=10\sqrt{31}$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-10\sqrt{31}}{2*-5}=\frac{40-10\sqrt{31}}{-10}
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+10\sqrt{31}}{2*-5}=\frac{40+10\sqrt{31}}{-10}
$