6/7t-12=13/14t+15

Solution for 6/7t-12=13/14t+15 equation:

6/7t-12=13/14t+15

We move all terms to the left:

6/7t-12-(13/14t+15)=0


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R



Domain of the equation: 14t+15)!=0

t∈R


We get rid of parentheses

6/7t-13/14t-15-12=0

We calculate fractions


84t/98t^2+(-91t)/98t^2-15-12=0

We add all the numbers together, and all the variables

84t/98t^2+(-91t)/98t^2-27=0

We multiply all the terms by the denominator


84t+(-91t)-27*98t^2=0

Wy multiply elements

-2646t^2+84t+(-91t)=0

We get rid of parentheses

-2646t^2+84t-91t=0

We add all the numbers together, and all the variables

-2646t^2-7t=0

a = -2646; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-2646)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-2646}=\frac{0}{-5292}
=0
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-2646}=\frac{14}{-5292}
=-1/378
$