9x+1/5x=80

Solution for 9x+1/5x=80 equation:

9x+1/5x=80

We move all terms to the left:

9x+1/5x-(80)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


9x*5x-80*5x+1=0

Wy multiply elements

45x^2-400x+1=0

a = 45; b = -400; c = +1;
Δ = b2-4ac
Δ = -4002-4·45·1
Δ = 159820
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:

$\sqrt{\Delta}=\sqrt{159820}=\sqrt{4*39955}=\sqrt{4}*\sqrt{39955}=2\sqrt{39955}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-400)-2\sqrt{39955}}{2*45}=\frac{400-2\sqrt{39955}}{90}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-400)+2\sqrt{39955}}{2*45}=\frac{400+2\sqrt{39955}}{90}
$