40=-4.9t^2+30t

Solution for 40=-4.9t^2+30t equation:

40=-4.9t^2+30t

We move all terms to the left:

40-(-4.9t^2+30t)=0

We get rid of parentheses

4.9t^2-30t+40=0

a = 4.9; b = -30; c = +40;
Δ = b2-4ac
Δ = -302-4·4.9·40
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{29}}{2*4.9}=\frac{30-2\sqrt{29}}{9.8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{29}}{2*4.9}=\frac{30+2\sqrt{29}}{9.8}
$