6x-4/9x=1

Solution for 6x-4/9x=1 equation:

6x-4/9x=1

We move all terms to the left:

6x-4/9x-(1)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


6x*9x-1*9x-4=0

Wy multiply elements

54x^2-9x-4=0

a = 54; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·54·(-4)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{105}}{2*54}=\frac{9-3\sqrt{105}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{105}}{2*54}=\frac{9+3\sqrt{105}}{108}
$