37t-2.0t^2=100

Solution for 37t-2.0t^2=100 equation:

37t-2.0t^2=100

We move all terms to the left:

37t-2.0t^2-(100)=0

We add all the numbers together, and all the variables

-2t^2+37t-100=0

a = -2; b = 37; c = -100;
Δ = b2-4ac
Δ = 372-4·(-2)·(-100)
Δ = 569
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{569}}{2*-2}=\frac{-37-\sqrt{569}}{-4}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{569}}{2*-2}=\frac{-37+\sqrt{569}}{-4}
$