7/3t+6/t=1

Solution for 7/3t+6/t=1 equation:

7/3t+6/t=1

We move all terms to the left:

7/3t+6/t-(1)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: t!=0

t∈R


We calculate fractions


7t/3t^2+18t/3t^2-1=0

We multiply all the terms by the denominator


7t+18t-1*3t^2=0

We add all the numbers together, and all the variables

25t-1*3t^2=0

Wy multiply elements

-3t^2+25t=0

a = -3; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·(-3)·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*-3}=\frac{-50}{-6}
=8+1/3
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*-3}=\frac{0}{-6}
=0
$