5t2+30t=60

Solution for 5t2+30t=60 equation:

5t^2+30t=60

We move all terms to the left:

5t^2+30t-(60)=0

a = 5; b = 30; c = -60;
Δ = b2-4ac
Δ = 302-4·5·(-60)
Δ = 2100
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:

$\sqrt{\Delta}=\sqrt{2100}=\sqrt{100*21}=\sqrt{100}*\sqrt{21}=10\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{21}}{2*5}=\frac{-30-10\sqrt{21}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{21}}{2*5}=\frac{-30+10\sqrt{21}}{10}
$