200=6t^2-45t+74

Solution for 200=6t^2-45t+74 equation:

200=6t^2-45t+74

We move all terms to the left:

200-(6t^2-45t+74)=0

We get rid of parentheses

-6t^2+45t-74+200=0

We add all the numbers together, and all the variables

-6t^2+45t+126=0

a = -6; b = 45; c = +126;
Δ = b2-4ac
Δ = 452-4·(-6)·126
Δ = 5049
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:

$\sqrt{\Delta}=\sqrt{5049}=\sqrt{9*561}=\sqrt{9}*\sqrt{561}=3\sqrt{561}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{561}}{2*-6}=\frac{-45-3\sqrt{561}}{-12}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{561}}{2*-6}=\frac{-45+3\sqrt{561}}{-12}
$