6/7t-12=3/4t+15

Solution for 6/7t-12=3/4t+15 equation:

6/7t-12=3/4t+15

We move all terms to the left:

6/7t-12-(3/4t+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-3/4t-15-12=0

We calculate fractions


24t/28t^2+(-21t)/28t^2-15-12=0

We add all the numbers together, and all the variables

24t/28t^2+(-21t)/28t^2-27=0

We multiply all the terms by the denominator


24t+(-21t)-27*28t^2=0

Wy multiply elements

-756t^2+24t+(-21t)=0

We get rid of parentheses

-756t^2+24t-21t=0

We add all the numbers together, and all the variables

-756t^2+3t=0

a = -756; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-756)·0
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3}{2*-756}=\frac{-6}{-1512}
=1/252
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-756}=\frac{0}{-1512}
=0
$