0=70t^2+140t-80

Solution for 0=70t^2+140t-80 equation:

0=70t^2+140t-80

We move all terms to the left:

0-(70t^2+140t-80)=0

We add all the numbers together, and all the variables

-(70t^2+140t-80)=0

We get rid of parentheses

-70t^2-140t+80=0

a = -70; b = -140; c = +80;
Δ = b2-4ac
Δ = -1402-4·(-70)·80
Δ = 42000
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:

$\sqrt{\Delta}=\sqrt{42000}=\sqrt{400*105}=\sqrt{400}*\sqrt{105}=20\sqrt{105}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-20\sqrt{105}}{2*-70}=\frac{140-20\sqrt{105}}{-140}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+20\sqrt{105}}{2*-70}=\frac{140+20\sqrt{105}}{-140}
$