4/7a-2=1/3a+5

Solution for 4/7a-2=1/3a+5 equation:

4/7a-2=1/3a+5

We move all terms to the left:

4/7a-2-(1/3a+5)=0


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R



Domain of the equation: 3a+5)!=0

a∈R


We get rid of parentheses

4/7a-1/3a-5-2=0

We calculate fractions


12a/21a^2+(-7a)/21a^2-5-2=0

We add all the numbers together, and all the variables

12a/21a^2+(-7a)/21a^2-7=0

We multiply all the terms by the denominator


12a+(-7a)-7*21a^2=0

Wy multiply elements

-147a^2+12a+(-7a)=0

We get rid of parentheses

-147a^2+12a-7a=0

We add all the numbers together, and all the variables

-147a^2+5a=0

a = -147; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-147)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-147}=\frac{-10}{-294}
=5/147
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-147}=\frac{0}{-294}
=0
$