6/x=(2x+4)/5

Solution for 6/x=(2x+4)/5 equation:

6/x=(2x+4)/5

We move all terms to the left:

6/x-((2x+4)/5)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


()/5x^2+(-((2x+4)*x)/5x^2=0

We multiply all the terms by the denominator


(-((2x+4)*x)+()=0


We calculate terms in parentheses: +(-((2x+4)*x)+(), so:

-((2x+4)*x)+(

We add all the numbers together, and all the variables

-((2x+4)*x)


We calculate terms in parentheses: -((2x+4)*x), so:

(2x+4)*x

We multiply parentheses

2x^2+4x

Back to the equation:

-(2x^2+4x)


We get rid of parentheses

-2x^2-4x

Back to the equation:

+(-2x^2-4x)


We get rid of parentheses

-2x^2-4x=0

a = -2; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-2)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-2}=\frac{0}{-4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-2}=\frac{8}{-4}
=-2
$