60=4t+6t^2

Solution for 60=4t+6t^2 equation:

60=4t+6t^2

We move all terms to the left:

60-(4t+6t^2)=0

We get rid of parentheses

-6t^2-4t+60=0

a = -6; b = -4; c = +60;
Δ = b2-4ac
Δ = -42-4·(-6)·60
Δ = 1456
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:

$\sqrt{\Delta}=\sqrt{1456}=\sqrt{16*91}=\sqrt{16}*\sqrt{91}=4\sqrt{91}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{91}}{2*-6}=\frac{4-4\sqrt{91}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{91}}{2*-6}=\frac{4+4\sqrt{91}}{-12}
$