3t^2+8t=60

Solution for 3t^2+8t=60 equation:

3t^2+8t=60

We move all terms to the left:

3t^2+8t-(60)=0

a = 3; b = 8; c = -60;
Δ = b2-4ac
Δ = 82-4·3·(-60)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-28}{2*3}=\frac{-36}{6}
=-6
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+28}{2*3}=\frac{20}{6}
=3+1/3
$