27=16t^2-37t-7

Solution for 27=16t^2-37t-7 equation:

27=16t^2-37t-7

We move all terms to the left:

27-(16t^2-37t-7)=0

We get rid of parentheses

-16t^2+37t+7+27=0

We add all the numbers together, and all the variables

-16t^2+37t+34=0

a = -16; b = 37; c = +34;
Δ = b2-4ac
Δ = 372-4·(-16)·34
Δ = 3545
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{3545}}{2*-16}=\frac{-37-\sqrt{3545}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{3545}}{2*-16}=\frac{-37+\sqrt{3545}}{-32}
$