3x+1/5x=26

Solution for 3x+1/5x=26 equation:

3x+1/5x=26

We move all terms to the left:

3x+1/5x-(26)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We multiply all the terms by the denominator


3x*5x-26*5x+1=0

Wy multiply elements

15x^2-130x+1=0

a = 15; b = -130; c = +1;
Δ = b2-4ac
Δ = -1302-4·15·1
Δ = 16840
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:

$\sqrt{\Delta}=\sqrt{16840}=\sqrt{4*4210}=\sqrt{4}*\sqrt{4210}=2\sqrt{4210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-130)-2\sqrt{4210}}{2*15}=\frac{130-2\sqrt{4210}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-130)+2\sqrt{4210}}{2*15}=\frac{130+2\sqrt{4210}}{30}
$