6/7t-12=3/14t+14

Solution for 6/7t-12=3/14t+14 equation:

6/7t-12=3/14t+14

We move all terms to the left:

6/7t-12-(3/14t+14)=0


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R



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

t∈R


We get rid of parentheses

6/7t-3/14t-14-12=0

We calculate fractions


84t/98t^2+(-21t)/98t^2-14-12=0

We add all the numbers together, and all the variables

84t/98t^2+(-21t)/98t^2-26=0

We multiply all the terms by the denominator


84t+(-21t)-26*98t^2=0

Wy multiply elements

-2548t^2+84t+(-21t)=0

We get rid of parentheses

-2548t^2+84t-21t=0

We add all the numbers together, and all the variables

-2548t^2+63t=0

a = -2548; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-2548)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-2548}=\frac{-126}{-5096}
=9/364
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-2548}=\frac{0}{-5096}
=0
$