-7/11a+2=3-5/22a

Solution for -7/11a+2=3-5/22a equation:

-7/11a+2=3-5/22a

We move all terms to the left:

-7/11a+2-(3-5/22a)=0


Domain of the equation: 11a!=0

a!=0/11

a!=0

a∈R



Domain of the equation: 22a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

-7/11a-(-5/22a+3)+2=0

We get rid of parentheses

-7/11a+5/22a-3+2=0

We calculate fractions


(-154a)/242a^2+55a/242a^2-3+2=0

We add all the numbers together, and all the variables

(-154a)/242a^2+55a/242a^2-1=0

We multiply all the terms by the denominator


(-154a)+55a-1*242a^2=0

We add all the numbers together, and all the variables

55a+(-154a)-1*242a^2=0

Wy multiply elements

-242a^2+55a+(-154a)=0

We get rid of parentheses

-242a^2+55a-154a=0

We add all the numbers together, and all the variables

-242a^2-99a=0

a = -242; b = -99; c = 0;
Δ = b2-4ac
Δ = -992-4·(-242)·0
Δ = 9801
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9801}=99$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-99)-99}{2*-242}=\frac{0}{-484}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-99)+99}{2*-242}=\frac{198}{-484}
=-9/22
$