0=70-10t-5t2

Solution for 0=70-10t-5t2 equation:

0=70-10t-5t^2

We move all terms to the left:

0-(70-10t-5t^2)=0

We add all the numbers together, and all the variables

-(70-10t-5t^2)=0

We get rid of parentheses

5t^2+10t-70=0

a = 5; b = 10; c = -70;
Δ = b2-4ac
Δ = 102-4·5·(-70)
Δ = 1500
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:

$\sqrt{\Delta}=\sqrt{1500}=\sqrt{100*15}=\sqrt{100}*\sqrt{15}=10\sqrt{15}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{15}}{2*5}=\frac{-10-10\sqrt{15}}{10}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{15}}{2*5}=\frac{-10+10\sqrt{15}}{10}
$