0=70t^2+140t-50

Solution for 0=70t^2+140t-50 equation:

0=70t^2+140t-50

We move all terms to the left:

0-(70t^2+140t-50)=0

We add all the numbers together, and all the variables

-(70t^2+140t-50)=0

We get rid of parentheses

-70t^2-140t+50=0

a = -70; b = -140; c = +50;
Δ = b2-4ac
Δ = -1402-4·(-70)·50
Δ = 33600
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:

$\sqrt{\Delta}=\sqrt{33600}=\sqrt{1600*21}=\sqrt{1600}*\sqrt{21}=40\sqrt{21}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-40\sqrt{21}}{2*-70}=\frac{140-40\sqrt{21}}{-140}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+40\sqrt{21}}{2*-70}=\frac{140+40\sqrt{21}}{-140}
$