70=12t+4.9t^2

Solution for 70=12t+4.9t^2 equation:

70=12t+4.9t^2

We move all terms to the left:

70-(12t+4.9t^2)=0

We get rid of parentheses

-4.9t^2-12t+70=0

a = -4.9; b = -12; c = +70;
Δ = b2-4ac
Δ = -122-4·(-4.9)·70
Δ = 1516
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:

$\sqrt{\Delta}=\sqrt{1516}=\sqrt{4*379}=\sqrt{4}*\sqrt{379}=2\sqrt{379}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{379}}{2*-4.9}=\frac{12-2\sqrt{379}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{379}}{2*-4.9}=\frac{12+2\sqrt{379}}{-9.8}
$