4/7a+2/3a=13

Solution for 4/7a+2/3a=13 equation:

4/7a+2/3a=13

We move all terms to the left:

4/7a+2/3a-(13)=0


Domain of the equation: 7a!=0

a!=0/7

a!=0

a∈R



Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R


We calculate fractions


12a/21a^2+14a/21a^2-13=0

We multiply all the terms by the denominator


12a+14a-13*21a^2=0

We add all the numbers together, and all the variables

26a-13*21a^2=0

Wy multiply elements

-273a^2+26a=0

a = -273; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-273)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-26}{2*-273}=\frac{-52}{-546}
=2/21
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-273}=\frac{0}{-546}
=0
$