1/8t+3/t-3=4

Solution for 1/8t+3/t-3=4 equation:

1/8t+3/t-3=4

We move all terms to the left:

1/8t+3/t-3-(4)=0


Domain of the equation: 8t!=0

t!=0/8

t!=0

t∈R



Domain of the equation: t!=0

t∈R


We add all the numbers together, and all the variables

1/8t+3/t-7=0

We calculate fractions


t/8t^2+24t/8t^2-7=0

We multiply all the terms by the denominator


t+24t-7*8t^2=0

We add all the numbers together, and all the variables

25t-7*8t^2=0

Wy multiply elements

-56t^2+25t=0

a = -56; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-56)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*-56}=\frac{-50}{-112}
=25/56
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-56}=\frac{0}{-112}
=0
$