10t^2-15t-40=0

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

10t^2-15t-40=0

a = 10; b = -15; c = -40;
Δ = b2-4ac
Δ = -152-4·10·(-40)
Δ = 1825
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:

$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{73}}{2*10}=\frac{15-5\sqrt{73}}{20}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{73}}{2*10}=\frac{15+5\sqrt{73}}{20}
$