22=2+37t+-16t2

Solution for 22=2+37t+-16t2 equation:

22=2+37t+-16t^2

We move all terms to the left:

22-(2+37t+-16t^2)=0

We use the square of the difference formula

-(2+37t-16t^2)+22=0

We get rid of parentheses

16t^2-37t-2+22=0

We add all the numbers together, and all the variables

16t^2-37t+20=0

a = 16; b = -37; c = +20;
Δ = b2-4ac
Δ = -372-4·16·20
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-37)-\sqrt{89}}{2*16}=\frac{37-\sqrt{89}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{89}}{2*16}=\frac{37+\sqrt{89}}{32}
$