12x+1/5x=9

Solution for 12x+1/5x=9 equation:

12x+1/5x=9

We move all terms to the left:

12x+1/5x-(9)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


12x*5x-9*5x+1=0

Wy multiply elements

60x^2-45x+1=0

a = 60; b = -45; c = +1;
Δ = b2-4ac
Δ = -452-4·60·1
Δ = 1785
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{1785}}{2*60}=\frac{45-\sqrt{1785}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{1785}}{2*60}=\frac{45+\sqrt{1785}}{120}
$