5/7t-12=3/14t+15

Solution for 5/7t-12=3/14t+15 equation:

5/7t-12=3/14t+15

We move all terms to the left:

5/7t-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 get rid of parentheses

5/7t-3/14t-15-12=0

We calculate fractions


70t/98t^2+(-21t)/98t^2-15-12=0

We add all the numbers together, and all the variables

70t/98t^2+(-21t)/98t^2-27=0

We multiply all the terms by the denominator


70t+(-21t)-27*98t^2=0

Wy multiply elements

-2646t^2+70t+(-21t)=0

We get rid of parentheses

-2646t^2+70t-21t=0

We add all the numbers together, and all the variables

-2646t^2+49t=0

a = -2646; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·(-2646)·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*-2646}=\frac{-98}{-5292}
=1/54
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*-2646}=\frac{0}{-5292}
=0
$