5x-2/9x-6=1

Solution for 5x-2/9x-6=1 equation:

5x-2/9x-6=1

We move all terms to the left:

5x-2/9x-6-(1)=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

5x-2/9x-7=0

We multiply all the terms by the denominator


5x*9x-7*9x-2=0

Wy multiply elements

45x^2-63x-2=0

a = 45; b = -63; c = -2;
Δ = b2-4ac
Δ = -632-4·45·(-2)
Δ = 4329
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:

$\sqrt{\Delta}=\sqrt{4329}=\sqrt{9*481}=\sqrt{9}*\sqrt{481}=3\sqrt{481}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{481}}{2*45}=\frac{63-3\sqrt{481}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{481}}{2*45}=\frac{63+3\sqrt{481}}{90}
$