6a-11=-2/3a

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

6a-11=-2/3a

We move all terms to the left:

6a-11-(-2/3a)=0


Domain of the equation: 3a)!=0

a!=0/1

a!=0

a∈R


We get rid of parentheses

6a+2/3a-11=0

We multiply all the terms by the denominator


6a*3a-11*3a+2=0

Wy multiply elements

18a^2-33a+2=0

a = 18; b = -33; c = +2;
Δ = b2-4ac
Δ = -332-4·18·2
Δ = 945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3\sqrt{105}}{2*18}=\frac{33-3\sqrt{105}}{36}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3\sqrt{105}}{2*18}=\frac{33+3\sqrt{105}}{36}
$