-16t^2+105t=34

Solution for -16t^2+105t=34 equation:

-16t^2+105t=34

We move all terms to the left:

-16t^2+105t-(34)=0

a = -16; b = 105; c = -34;
Δ = b2-4ac
Δ = 1052-4·(-16)·(-34)
Δ = 8849
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{-(105)-\sqrt{8849}}{2*-16}=\frac{-105-\sqrt{8849}}{-32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(105)+\sqrt{8849}}{2*-16}=\frac{-105+\sqrt{8849}}{-32}
$