10/5x-18=20/2x+4

Solution for 10/5x-18=20/2x+4 equation:

10/5x-18=20/2x+4

We move all terms to the left:

10/5x-18-(20/2x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

10/5x-20/2x-4-18=0

We calculate fractions


20x/10x^2+(-100x)/10x^2-4-18=0

We add all the numbers together, and all the variables

20x/10x^2+(-100x)/10x^2-22=0

We multiply all the terms by the denominator


20x+(-100x)-22*10x^2=0

Wy multiply elements

-220x^2+20x+(-100x)=0

We get rid of parentheses

-220x^2+20x-100x=0

We add all the numbers together, and all the variables

-220x^2-80x=0

a = -220; b = -80; c = 0;
Δ = b2-4ac
Δ = -802-4·(-220)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80}{2*-220}=\frac{0}{-440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80}{2*-220}=\frac{160}{-440}
=-4/11
$