6/7t+-12=3/14t+15

Solution for 6/7t+-12=3/14t+15 equation:

6/7t+-12=3/14t+15

We move all terms to the left:

6/7t+-12-(3/14t+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 add all the numbers together, and all the variables

6/7t-(3/14t+15)=0

We get rid of parentheses

6/7t-3/14t-15=0

We calculate fractions


84t/98t^2+(-21t)/98t^2-15=0

We multiply all the terms by the denominator


84t+(-21t)-15*98t^2=0

Wy multiply elements

-1470t^2+84t+(-21t)=0

We get rid of parentheses

-1470t^2+84t-21t=0

We add all the numbers together, and all the variables

-1470t^2+63t=0

a = -1470; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-1470)·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*-1470}=\frac{-126}{-2940}
=3/70
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-1470}=\frac{0}{-2940}
=0
$