9x-1/5x=18

Solution for 9x-1/5x=18 equation:

9x-1/5x=18

We move all terms to the left:

9x-1/5x-(18)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


9x*5x-18*5x-1=0

Wy multiply elements

45x^2-90x-1=0

a = 45; b = -90; c = -1;
Δ = b2-4ac
Δ = -902-4·45·(-1)
Δ = 8280
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:

$\sqrt{\Delta}=\sqrt{8280}=\sqrt{36*230}=\sqrt{36}*\sqrt{230}=6\sqrt{230}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{230}}{2*45}=\frac{90-6\sqrt{230}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{230}}{2*45}=\frac{90+6\sqrt{230}}{90}
$