420.5=t^2+60t

Solution for 420.5=t^2+60t equation:

420.5=t^2+60t

We move all terms to the left:

420.5-(t^2+60t)=0

We get rid of parentheses

-t^2-60t+420.5=0

We add all the numbers together, and all the variables

-1t^2-60t+420.5=0

a = -1; b = -60; c = +420.5;
Δ = b2-4ac
Δ = -602-4·(-1)·420.5
Δ = 5282
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{-(-60)-\sqrt{5282}}{2*-1}=\frac{60-\sqrt{5282}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+\sqrt{5282}}{2*-1}=\frac{60+\sqrt{5282}}{-2}
$