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

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

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

We move all terms to the left:

6/7t-12-(3/12t+15)=0


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R



Domain of the equation: 12t+15)!=0

t∈R


We get rid of parentheses

6/7t-3/12t-15-12=0

We calculate fractions


72t/84t^2+(-21t)/84t^2-15-12=0

We add all the numbers together, and all the variables

72t/84t^2+(-21t)/84t^2-27=0

We multiply all the terms by the denominator


72t+(-21t)-27*84t^2=0

Wy multiply elements

-2268t^2+72t+(-21t)=0

We get rid of parentheses

-2268t^2+72t-21t=0

We add all the numbers together, and all the variables

-2268t^2+51t=0

a = -2268; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-2268)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-2268}=\frac{-102}{-4536}
=17/756
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-2268}=\frac{0}{-4536}
=0
$