(34x+7)/x=5x

Solution for (34x+7)/x=5x equation:

(34x+7)/x=5x

We move all terms to the left:

(34x+7)/x-(5x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-5x+(34x+7)/x=0

We multiply all the terms by the denominator


-5x*x+(34x+7)=0

Wy multiply elements

-5x^2+(34x+7)=0

We get rid of parentheses

-5x^2+34x+7=0

a = -5; b = 34; c = +7;
Δ = b2-4ac
Δ = 342-4·(-5)·7
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-36}{2*-5}=\frac{-70}{-10}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+36}{2*-5}=\frac{2}{-10}
=-1/5
$