90=4.9t^2+42t

Solution for 90=4.9t^2+42t equation:

90=4.9t^2+42t

We move all terms to the left:

90-(4.9t^2+42t)=0

We get rid of parentheses

-4.9t^2-42t+90=0

a = -4.9; b = -42; c = +90;
Δ = b2-4ac
Δ = -422-4·(-4.9)·90
Δ = 3528
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:

$\sqrt{\Delta}=\sqrt{3528}=\sqrt{1764*2}=\sqrt{1764}*\sqrt{2}=42\sqrt{2}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-42\sqrt{2}}{2*-4.9}=\frac{42-42\sqrt{2}}{-9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+42\sqrt{2}}{2*-4.9}=\frac{42+42\sqrt{2}}{-9.8}
$