5/3t+5=2/7t+14

Solution for 5/3t+5=2/7t+14 equation:

5/3t+5=2/7t+14

We move all terms to the left:

5/3t+5-(2/7t+14)=0


Domain of the equation: 3t!=0

t!=0/3

t!=0

t∈R



Domain of the equation: 7t+14)!=0

t∈R


We get rid of parentheses

5/3t-2/7t-14+5=0

We calculate fractions


35t/21t^2+(-6t)/21t^2-14+5=0

We add all the numbers together, and all the variables

35t/21t^2+(-6t)/21t^2-9=0

We multiply all the terms by the denominator


35t+(-6t)-9*21t^2=0

Wy multiply elements

-189t^2+35t+(-6t)=0

We get rid of parentheses

-189t^2+35t-6t=0

We add all the numbers together, and all the variables

-189t^2+29t=0

a = -189; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-189)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-189}=\frac{-58}{-378}
=29/189
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-189}=\frac{0}{-378}
=0
$