7.5t^2+30t-120=0

Solution for 7.5t^2+30t-120=0 equation:

7.5t^2+30t-120=0

a = 7.5; b = 30; c = -120;
Δ = b2-4ac
Δ = 302-4·7.5·(-120)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30\sqrt{5}}{2*7.5}=\frac{-30-30\sqrt{5}}{15}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30\sqrt{5}}{2*7.5}=\frac{-30+30\sqrt{5}}{15}
$