0=60t+-5t2

Solution for 0=60t+-5t2 equation:

0=60t+-5t^2

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We use the square of the difference formula

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

We get rid of parentheses

5t^2-60t=0

a = 5; b = -60; c = 0;
Δ = b2-4ac
Δ = -602-4·5·0
Δ = 3600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3600}=60$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-60}{2*5}=\frac{0}{10}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+60}{2*5}=\frac{120}{10}
=12
$