5/16x-2=2+7/20x

Solution for 5/16x-2=2+7/20x equation:

5/16x-2=2+7/20x

We move all terms to the left:

5/16x-2-(2+7/20x)=0


Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R



Domain of the equation: 20x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

5/16x-(7/20x+2)-2=0

We get rid of parentheses

5/16x-7/20x-2-2=0

We calculate fractions


100x/320x^2+(-112x)/320x^2-2-2=0

We add all the numbers together, and all the variables

100x/320x^2+(-112x)/320x^2-4=0

We multiply all the terms by the denominator


100x+(-112x)-4*320x^2=0

Wy multiply elements

-1280x^2+100x+(-112x)=0

We get rid of parentheses

-1280x^2+100x-112x=0

We add all the numbers together, and all the variables

-1280x^2-12x=0

a = -1280; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-1280)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*-1280}=\frac{0}{-2560}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-1280}=\frac{24}{-2560}
=-3/320
$