0=40t-15t^2-10

Solution for 0=40t-15t^2-10 equation:

0=40t-15t^2-10

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

15t^2-40t+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}
$