5/7a-5=2/3a+1

Solution for 5/7a-5=2/3a+1 equation:

5/7a-5=2/3a+1

We move all terms to the left:

5/7a-5-(2/3a+1)=0


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R



Domain of the equation: 3a+1)!=0

a∈R


We get rid of parentheses

5/7a-2/3a-1-5=0

We calculate fractions


15a/21a^2+(-14a)/21a^2-1-5=0

We add all the numbers together, and all the variables

15a/21a^2+(-14a)/21a^2-6=0

We multiply all the terms by the denominator


15a+(-14a)-6*21a^2=0

Wy multiply elements

-126a^2+15a+(-14a)=0

We get rid of parentheses

-126a^2+15a-14a=0

We add all the numbers together, and all the variables

-126a^2+a=0

a = -126; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-126)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-126}=\frac{-2}{-252}
=1/126
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-126}=\frac{0}{-252}
=0
$