(3/47x)+37=5x+62

Solution for (3/47x)+37=5x+62 equation:

(3/47x)+37=5x+62

We move all terms to the left:

(3/47x)+37-(5x+62)=0


Domain of the equation: 47x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/47x)-(5x+62)+37=0

We get rid of parentheses

3/47x-5x-62+37=0

We multiply all the terms by the denominator


-5x*47x-62*47x+37*47x+3=0

Wy multiply elements

-235x^2-2914x+1739x+3=0

We add all the numbers together, and all the variables

-235x^2-1175x+3=0

a = -235; b = -1175; c = +3;
Δ = b2-4ac
Δ = -11752-4·(-235)·3
Δ = 1383445
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:

$\sqrt{\Delta}=\sqrt{1383445}=\sqrt{841*1645}=\sqrt{841}*\sqrt{1645}=29\sqrt{1645}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1175)-29\sqrt{1645}}{2*-235}=\frac{1175-29\sqrt{1645}}{-470}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1175)+29\sqrt{1645}}{2*-235}=\frac{1175+29\sqrt{1645}}{-470}
$