2/3a+11=26-1/6a

Solution for 2/3a+11=26-1/6a equation:

2/3a+11=26-1/6a

We move all terms to the left:

2/3a+11-(26-1/6a)=0


Domain of the equation: 3a!=0

a!=0/3

a!=0

a∈R



Domain of the equation: 6a)!=0

a!=0/1

a!=0

a∈R


We add all the numbers together, and all the variables

2/3a-(-1/6a+26)+11=0

We get rid of parentheses

2/3a+1/6a-26+11=0

We calculate fractions


12a/18a^2+3a/18a^2-26+11=0

We add all the numbers together, and all the variables

12a/18a^2+3a/18a^2-15=0

We multiply all the terms by the denominator


12a+3a-15*18a^2=0

We add all the numbers together, and all the variables

15a-15*18a^2=0

Wy multiply elements

-270a^2+15a=0

a = -270; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-270)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-270}=\frac{-30}{-540}
=1/18
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-270}=\frac{0}{-540}
=0
$