7x-3/9x-1=0

Solution for 7x-3/9x-1=0 equation:

7x-3/9x-1=0


Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We multiply all the terms by the denominator


7x*9x-1*9x-3=0

Wy multiply elements

63x^2-9x-3=0

a = 63; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·63·(-3)
Δ = 837
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:

$\sqrt{\Delta}=\sqrt{837}=\sqrt{9*93}=\sqrt{9}*\sqrt{93}=3\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{93}}{2*63}=\frac{9-3\sqrt{93}}{126}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{93}}{2*63}=\frac{9+3\sqrt{93}}{126}
$