(5x)+(18.5/3x)=29.70

Solution for (5x)+(18.5/3x)=29.70 equation:

(5x)+(18.5/3x)=29.70

We move all terms to the left:

(5x)+(18.5/3x)-(29.70)=0


Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5x+(+18.5/3x)-(29.7)=0

We add all the numbers together, and all the variables

5x+(+18.5/3x)-29.7=0

We get rid of parentheses

5x+18.5/3x-29.7=0

We multiply all the terms by the denominator


5x*3x-(29.7)*3x+18.5=0

We multiply parentheses

5x*3x-89.1x+18.5=0

Wy multiply elements

15x^2-89.1x+18.5=0

a = 15; b = -89.1; c = +18.5;
Δ = b2-4ac
Δ = -89.12-4·15·18.5
Δ = 6828.81
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{-(-89.1)-\sqrt{6828.81}}{2*15}=\frac{89.1-\sqrt{6828.81}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-89.1)+\sqrt{6828.81}}{2*15}=\frac{89.1+\sqrt{6828.81}}{30}
$