140=t^2+140t+30

Solution for 140=t^2+140t+30 equation:

140=t^2+140t+30

We move all terms to the left:

140-(t^2+140t+30)=0

We get rid of parentheses

-t^2-140t-30+140=0

We add all the numbers together, and all the variables

-1t^2-140t+110=0

a = -1; b = -140; c = +110;
Δ = b2-4ac
Δ = -1402-4·(-1)·110
Δ = 20040
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:

$\sqrt{\Delta}=\sqrt{20040}=\sqrt{4*5010}=\sqrt{4}*\sqrt{5010}=2\sqrt{5010}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{5010}}{2*-1}=\frac{140-2\sqrt{5010}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{5010}}{2*-1}=\frac{140+2\sqrt{5010}}{-2}
$