5t=60-5t^2

Solution for 5t=60-5t^2 equation:

5t=60-5t^2

We move all terms to the left:

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

We get rid of parentheses

5t^2+5t-60=0

a = 5; b = 5; c = -60;
Δ = b2-4ac
Δ = 52-4·5·(-60)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-35}{2*5}=\frac{-40}{10}
=-4
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+35}{2*5}=\frac{30}{10}
=3
$