7.5t^2-10t-120=0

Solution for 7.5t^2-10t-120=0 equation:

7.5t^2-10t-120=0

a = 7.5; b = -10; c = -120;
Δ = b2-4ac
Δ = -102-4·7.5·(-120)
Δ = 3700
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:

$\sqrt{\Delta}=\sqrt{3700}=\sqrt{100*37}=\sqrt{100}*\sqrt{37}=10\sqrt{37}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10\sqrt{37}}{2*7.5}=\frac{10-10\sqrt{37}}{15}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10\sqrt{37}}{2*7.5}=\frac{10+10\sqrt{37}}{15}
$