2/7t-12=3/12t+15

Solution for 2/7t-12=3/12t+15 equation:

2/7t-12=3/12t+15

We move all terms to the left:

2/7t-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

2/7t-3/12t-15-12=0

We calculate fractions


24t/84t^2+(-21t)/84t^2-15-12=0

We add all the numbers together, and all the variables

24t/84t^2+(-21t)/84t^2-27=0

We multiply all the terms by the denominator


24t+(-21t)-27*84t^2=0

Wy multiply elements

-2268t^2+24t+(-21t)=0

We get rid of parentheses

-2268t^2+24t-21t=0

We add all the numbers together, and all the variables

-2268t^2+3t=0

a = -2268; b = 3; c = 0;
Δ = b2-4ac
Δ = 32-4·(-2268)·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*-2268}=\frac{-6}{-4536}
=1/756
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3}{2*-2268}=\frac{0}{-4536}
=0
$