60=5t^2+7t

Solution for 60=5t^2+7t equation:

60=5t^2+7t

We move all terms to the left:

60-(5t^2+7t)=0

We get rid of parentheses

-5t^2-7t+60=0

a = -5; b = -7; c = +60;
Δ = b2-4ac
Δ = -72-4·(-5)·60
Δ = 1249
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{1249}}{2*-5}=\frac{7-\sqrt{1249}}{-10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{1249}}{2*-5}=\frac{7+\sqrt{1249}}{-10}
$