-17t^2-51t=0

Solution for -17t^2-51t=0 equation:

-17t^2-51t=0

a = -17; b = -51; c = 0;
Δ = b2-4ac
Δ = -512-4·(-17)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-51}{2*-17}=\frac{0}{-34}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+51}{2*-17}=\frac{102}{-34}
=-3
$