240=15t+10t^2

Solution for 240=15t+10t^2 equation:

240=15t+10t^2

We move all terms to the left:

240-(15t+10t^2)=0

We get rid of parentheses

-10t^2-15t+240=0

a = -10; b = -15; c = +240;
Δ = b2-4ac
Δ = -152-4·(-10)·240
Δ = 9825
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:

$\sqrt{\Delta}=\sqrt{9825}=\sqrt{25*393}=\sqrt{25}*\sqrt{393}=5\sqrt{393}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{393}}{2*-10}=\frac{15-5\sqrt{393}}{-20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{393}}{2*-10}=\frac{15+5\sqrt{393}}{-20}
$