6/7t-12=13/4t+15

Solution for 6/7t-12=13/4t+15 equation:

6/7t-12=13/4t+15

We move all terms to the left:

6/7t-12-(13/4t+15)=0


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R



Domain of the equation: 4t+15)!=0

t∈R


We get rid of parentheses

6/7t-13/4t-15-12=0

We calculate fractions


24t/28t^2+(-91t)/28t^2-15-12=0

We add all the numbers together, and all the variables

24t/28t^2+(-91t)/28t^2-27=0

We multiply all the terms by the denominator


24t+(-91t)-27*28t^2=0

Wy multiply elements

-756t^2+24t+(-91t)=0

We get rid of parentheses

-756t^2+24t-91t=0

We add all the numbers together, and all the variables

-756t^2-67t=0

a = -756; b = -67; c = 0;
Δ = b2-4ac
Δ = -672-4·(-756)·0
Δ = 4489
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4489}=67$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-67)-67}{2*-756}=\frac{0}{-1512}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+67}{2*-756}=\frac{134}{-1512}
=-67/756
$