6x-11=2/9x-1

Solution for 6x-11=2/9x-1 equation:

6x-11=2/9x-1

We move all terms to the left:

6x-11-(2/9x-1)=0


Domain of the equation: 9x-1)!=0

x∈R


We get rid of parentheses

6x-2/9x+1-11=0

We multiply all the terms by the denominator


6x*9x+1*9x-11*9x-2=0

Wy multiply elements

54x^2+9x-99x-2=0

We add all the numbers together, and all the variables

54x^2-90x-2=0

a = 54; b = -90; c = -2;
Δ = b2-4ac
Δ = -902-4·54·(-2)
Δ = 8532
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{8532}=\sqrt{36*237}=\sqrt{36}*\sqrt{237}=6\sqrt{237}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{237}}{2*54}=\frac{90-6\sqrt{237}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{237}}{2*54}=\frac{90+6\sqrt{237}}{108}
$