3x+7=20/x

Solution for 3x+7=20/x equation:

3x+7=20/x

We move all terms to the left:

3x+7-(20/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+20/x)+7=0

We get rid of parentheses

3x-20/x+7=0

We multiply all the terms by the denominator


3x*x+7*x-20=0

We add all the numbers together, and all the variables

7x+3x*x-20=0

Wy multiply elements

3x^2+7x-20=0

a = 3; b = 7; c = -20;
Δ = b2-4ac
Δ = 72-4·3·(-20)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-17}{2*3}=\frac{-24}{6}
=-4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+17}{2*3}=\frac{10}{6}
=1+2/3
$