5t^2+54t-120=0

Solution for 5t^2+54t-120=0 equation:

5t^2+54t-120=0

a = 5; b = 54; c = -120;
Δ = b2-4ac
Δ = 542-4·5·(-120)
Δ = 5316
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:

$\sqrt{\Delta}=\sqrt{5316}=\sqrt{4*1329}=\sqrt{4}*\sqrt{1329}=2\sqrt{1329}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{1329}}{2*5}=\frac{-54-2\sqrt{1329}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{1329}}{2*5}=\frac{-54+2\sqrt{1329}}{10}
$