t2-40t-80=0

Solution for t2-40t-80=0 equation:

t2-40t-80=0

We add all the numbers together, and all the variables

t^2-40t-80=0

a = 1; b = -40; c = -80;
Δ = b2-4ac
Δ = -402-4·1·(-80)
Δ = 1920
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:

$\sqrt{\Delta}=\sqrt{1920}=\sqrt{64*30}=\sqrt{64}*\sqrt{30}=8\sqrt{30}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{30}}{2*1}=\frac{40-8\sqrt{30}}{2}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{30}}{2*1}=\frac{40+8\sqrt{30}}{2}
$