1/6t+1/8t=500

Solution for 1/6t+1/8t=500 equation:

1/6t+1/8t=500

We move all terms to the left:

1/6t+1/8t-(500)=0


Domain of the equation: 6t!=0

t!=0/6

t!=0

t∈R



Domain of the equation: 8t!=0

t!=0/8

t!=0

t∈R


We calculate fractions


8t/48t^2+6t/48t^2-500=0

We multiply all the terms by the denominator


8t+6t-500*48t^2=0

We add all the numbers together, and all the variables

14t-500*48t^2=0

Wy multiply elements

-24000t^2+14t=0

a = -24000; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·(-24000)·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*-24000}=\frac{-28}{-48000}
=7/12000
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*-24000}=\frac{0}{-48000}
=0
$