80-40t/t^2=5

Solution for 80-40t/t^2=5 equation:

80-40t/t^2=5

We move all terms to the left:

80-40t/t^2-(5)=0


Domain of the equation: t^2!=0

t^2!=0/

t^2!=√0

t!=0

t∈R


We add all the numbers together, and all the variables

-40t/t^2+75=0

We multiply all the terms by the denominator


-40t+75*t^2=0

We add all the numbers together, and all the variables

75t^2-40t=0

a = 75; b = -40; c = 0;
Δ = b2-4ac
Δ = -402-4·75·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40}{2*75}=\frac{0}{150}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40}{2*75}=\frac{80}{150}
=8/15
$