10=140+60t-5t^2

Solution for 10=140+60t-5t^2 equation:

10=140+60t-5t^2

We move all terms to the left:

10-(140+60t-5t^2)=0

We get rid of parentheses

5t^2-60t-140+10=0

We add all the numbers together, and all the variables

5t^2-60t-130=0

a = 5; b = -60; c = -130;
Δ = b2-4ac
Δ = -602-4·5·(-130)
Δ = 6200
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:

$\sqrt{\Delta}=\sqrt{6200}=\sqrt{100*62}=\sqrt{100}*\sqrt{62}=10\sqrt{62}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-10\sqrt{62}}{2*5}=\frac{60-10\sqrt{62}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+10\sqrt{62}}{2*5}=\frac{60+10\sqrt{62}}{10}
$