40=-16t^2+90t

Solution for 40=-16t^2+90t equation:

40=-16t^2+90t

We move all terms to the left:

40-(-16t^2+90t)=0

We get rid of parentheses

16t^2-90t+40=0

a = 16; b = -90; c = +40;
Δ = b2-4ac
Δ = -902-4·16·40
Δ = 5540
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:

$\sqrt{\Delta}=\sqrt{5540}=\sqrt{4*1385}=\sqrt{4}*\sqrt{1385}=2\sqrt{1385}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{1385}}{2*16}=\frac{90-2\sqrt{1385}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{1385}}{2*16}=\frac{90+2\sqrt{1385}}{32}
$