0=t^2-109t-1675

Solution for 0=t^2-109t-1675 equation:

0=t^2-109t-1675

We move all terms to the left:

0-(t^2-109t-1675)=0

We add all the numbers together, and all the variables

-(t^2-109t-1675)=0

We get rid of parentheses

-t^2+109t+1675=0

We add all the numbers together, and all the variables

-1t^2+109t+1675=0

a = -1; b = 109; c = +1675;
Δ = b2-4ac
Δ = 1092-4·(-1)·1675
Δ = 18581
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{-(109)-\sqrt{18581}}{2*-1}=\frac{-109-\sqrt{18581}}{-2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(109)+\sqrt{18581}}{2*-1}=\frac{-109+\sqrt{18581}}{-2}
$