3/x=2(10x+10)/6(2*50)

Solution for 3/x=2(10x+10)/6(2*50) equation:

3/x=2(10x+10)/6(2*50)

We move all terms to the left:

3/x-(2(10x+10)/6(2*50))=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

3/x-(2(10x+10)/6100)=0

We calculate fractions


()/6100x^2+(-(2(10x+10)*x)/6100x^2=0

We multiply all the terms by the denominator


(-(2(10x+10)*x)+()=0


We calculate terms in parentheses: +(-(2(10x+10)*x)+(), so:

-(2(10x+10)*x)+(

We add all the numbers together, and all the variables

-(2(10x+10)*x)


We calculate terms in parentheses: -(2(10x+10)*x), so:

2(10x+10)*x

We multiply parentheses

20x^2+20x

Back to the equation:

-(20x^2+20x)


We get rid of parentheses

-20x^2-20x

Back to the equation:

+(-20x^2-20x)


We get rid of parentheses

-20x^2-20x=0

a = -20; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·(-20)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*-20}=\frac{0}{-40}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*-20}=\frac{40}{-40}
=-1
$