1/7a-3=-1/21a+2

Solution for 1/7a-3=-1/21a+2 equation:

1/7a-3=-1/21a+2

We move all terms to the left:

1/7a-3-(-1/21a+2)=0


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R



Domain of the equation: 21a+2)!=0

a∈R


We get rid of parentheses

1/7a+1/21a-2-3=0

We calculate fractions


21a/147a^2+7a/147a^2-2-3=0

We add all the numbers together, and all the variables

21a/147a^2+7a/147a^2-5=0

We multiply all the terms by the denominator


21a+7a-5*147a^2=0

We add all the numbers together, and all the variables

28a-5*147a^2=0

Wy multiply elements

-735a^2+28a=0

a = -735; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-735)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-735}=\frac{-56}{-1470}
=4/105
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-735}=\frac{0}{-1470}
=0
$