t2+80t-1000=0

Solution for t2+80t-1000=0 equation:

t2+80t-1000=0

We add all the numbers together, and all the variables

t^2+80t-1000=0

a = 1; b = 80; c = -1000;
Δ = b2-4ac
Δ = 802-4·1·(-1000)
Δ = 10400
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:

$\sqrt{\Delta}=\sqrt{10400}=\sqrt{400*26}=\sqrt{400}*\sqrt{26}=20\sqrt{26}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{26}}{2*1}=\frac{-80-20\sqrt{26}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{26}}{2*1}=\frac{-80+20\sqrt{26}}{2}
$