200=6t2-4.5t+74

Solution for 200=6t2-4.5t+74 equation:

200=6t^2-4.5t+74

We move all terms to the left:

200-(6t^2-4.5t+74)=0

We get rid of parentheses

-6t^2+4.5t-74+200=0

We add all the numbers together, and all the variables

-6t^2+4.5t+126=0

a = -6; b = 4.5; c = +126;
Δ = b2-4ac
Δ = 4.52-4·(-6)·126
Δ = 3044.25
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{-(4.5)-\sqrt{3044.25}}{2*-6}=\frac{-4.5-\sqrt{3044.25}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{3044.25}}{2*-6}=\frac{-4.5+\sqrt{3044.25}}{-12}
$