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

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

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

We move all terms to the left:

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


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R



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

t∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


-14t*7t+5*7t+5-2=0

We add all the numbers together, and all the variables

-14t*7t+5*7t+3=0

Wy multiply elements

-98t^2+35t+3=0

a = -98; b = 35; c = +3;
Δ = b2-4ac
Δ = 352-4·(-98)·3
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-49}{2*-98}=\frac{-84}{-196}
=3/7
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+49}{2*-98}=\frac{14}{-196}
=-1/14
$