0=-16t*t+6t+105

Solution for 0=-16t*t+6t+105 equation:

0=-16t*t+6t+105

We move all terms to the left:

0-(-16t*t+6t+105)=0

We add all the numbers together, and all the variables

-(6t-16t*t+105)+0=0

We add all the numbers together, and all the variables

-(6t-16t*t+105)=0

We get rid of parentheses

-6t+16t*t-105=0

Wy multiply elements

16t^2-6t-105=0

a = 16; b = -6; c = -105;
Δ = b2-4ac
Δ = -62-4·16·(-105)
Δ = 6756
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:

$\sqrt{\Delta}=\sqrt{6756}=\sqrt{4*1689}=\sqrt{4}*\sqrt{1689}=2\sqrt{1689}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{1689}}{2*16}=\frac{6-2\sqrt{1689}}{32}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{1689}}{2*16}=\frac{6+2\sqrt{1689}}{32}
$