9x-5/5x=3

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

9x-5/5x=3

We move all terms to the left:

9x-5/5x-(3)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


9x*5x-3*5x-5=0

Wy multiply elements

45x^2-15x-5=0

a = 45; b = -15; c = -5;
Δ = b2-4ac
Δ = -152-4·45·(-5)
Δ = 1125
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:

$\sqrt{\Delta}=\sqrt{1125}=\sqrt{225*5}=\sqrt{225}*\sqrt{5}=15\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15\sqrt{5}}{2*45}=\frac{15-15\sqrt{5}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15\sqrt{5}}{2*45}=\frac{15+15\sqrt{5}}{90}
$