3/x=(x+5)/2

Solution for 3/x=(x+5)/2 equation:

3/x=(x+5)/2

We move all terms to the left:

3/x-((x+5)/2)=0


Domain of the equation: x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: +(-((x+5)*x)+(), so:

-((x+5)*x)+(

We add all the numbers together, and all the variables

-((x+5)*x)


We calculate terms in parentheses: -((x+5)*x), so:

(x+5)*x

We multiply parentheses

x^2+5x

Back to the equation:

-(x^2+5x)


We get rid of parentheses

-x^2-5x

We add all the numbers together, and all the variables

-1x^2-5x

Back to the equation:

+(-1x^2-5x)


We get rid of parentheses

-1x^2-5x=0

a = -1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-1)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-1}=\frac{10}{-2}
=-5
$