3/7t-3=7-15/21t

Solution for 3/7t-3=7-15/21t equation:

3/7t-3=7-15/21t

We move all terms to the left:

3/7t-3-(7-15/21t)=0


Domain of the equation: 7t!=0

t!=0/7

t!=0

t∈R



Domain of the equation: 21t)!=0

t!=0/1

t!=0

t∈R


We add all the numbers together, and all the variables

3/7t-(-15/21t+7)-3=0

We get rid of parentheses

3/7t+15/21t-7-3=0

We calculate fractions


63t/147t^2+105t/147t^2-7-3=0

We add all the numbers together, and all the variables

63t/147t^2+105t/147t^2-10=0

We multiply all the terms by the denominator


63t+105t-10*147t^2=0

We add all the numbers together, and all the variables

168t-10*147t^2=0

Wy multiply elements

-1470t^2+168t=0

a = -1470; b = 168; c = 0;
Δ = b2-4ac
Δ = 1682-4·(-1470)·0
Δ = 28224
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28224}=168$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(168)-168}{2*-1470}=\frac{-336}{-2940}
=4/35
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(168)+168}{2*-1470}=\frac{0}{-2940}
=0
$