20-1/22(2x)=101/22(x)

Solution for 20-1/22(2x)=101/22(x) equation:

20-1/22(2x)=101/22(x)

We move all terms to the left:

20-1/22(2x)-(101/22(x))=0


Domain of the equation: 222x!=0

x!=0/222

x!=0

x∈R



Domain of the equation: 22x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/222x-(+101/22x)+20=0

We get rid of parentheses

-1/222x-101/22x+20=0

We calculate fractions


(-22x)/4884x^2+(-22422x)/4884x^2+20=0

We multiply all the terms by the denominator


(-22x)+(-22422x)+20*4884x^2=0

Wy multiply elements

97680x^2+(-22x)+(-22422x)=0

We get rid of parentheses

97680x^2-22x-22422x=0

We add all the numbers together, and all the variables

97680x^2-22444x=0

a = 97680; b = -22444; c = 0;
Δ = b2-4ac
Δ = -224442-4·97680·0
Δ = 503733136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{503733136}=22444$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22444)-22444}{2*97680}=\frac{0}{195360}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22444)+22444}{2*97680}=\frac{44888}{195360}
=5611/24420
$