5x-3/9x+1=1

Solution for 5x-3/9x+1=1 equation:

5x-3/9x+1=1

We move all terms to the left:

5x-3/9x+1-(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-3/9x=0

We multiply all the terms by the denominator


5x*9x-3=0

Wy multiply elements

45x^2-3=0

a = 45; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·45·(-3)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{15}}{2*45}=\frac{0-6\sqrt{15}}{90}
=-\frac{6\sqrt{15}}{90}
=-\frac{\sqrt{15}}{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{15}}{2*45}=\frac{0+6\sqrt{15}}{90}
=\frac{6\sqrt{15}}{90}
=\frac{\sqrt{15}}{15}
$