3/1a-1=7/11a+9

Solution for 3/1a-1=7/11a+9 equation:

3/1a-1=7/11a+9

We move all terms to the left:

3/1a-1-(7/11a+9)=0


Domain of the equation: 1a!=0

a∈R



Domain of the equation: 11a+9)!=0

a∈R


We get rid of parentheses

3/1a-7/11a-9-1=0

We calculate fractions


33a/11a^2+(-7a)/11a^2-9-1=0

We add all the numbers together, and all the variables

33a/11a^2+(-7a)/11a^2-10=0

We multiply all the terms by the denominator


33a+(-7a)-10*11a^2=0

Wy multiply elements

-110a^2+33a+(-7a)=0

We get rid of parentheses

-110a^2+33a-7a=0

We add all the numbers together, and all the variables

-110a^2+26a=0

a = -110; b = 26; c = 0;
Δ = b2-4ac
Δ = 262-4·(-110)·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*-110}=\frac{-52}{-220}
=13/55
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+26}{2*-110}=\frac{0}{-220}
=0
$