40t-15t^2=10

Solution for 40t-15t^2=10 equation:

40t-15t^2=10

We move all terms to the left:

40t-15t^2-(10)=0

a = -15; b = 40; c = -10;
Δ = b2-4ac
Δ = 402-4·(-15)·(-10)
Δ = 1000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-10\sqrt{10}}{2*-15}=\frac{-40-10\sqrt{10}}{-30}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+10\sqrt{10}}{2*-15}=\frac{-40+10\sqrt{10}}{-30}
$