40-1/22(4x)=30-1/22(3x)

Solution for 40-1/22(4x)=30-1/22(3x) equation:

40-1/22(4x)=30-1/22(3x)

We move all terms to the left:

40-1/22(4x)-(30-1/22(3x))=0


Domain of the equation: 224x!=0

x!=0/224

x!=0

x∈R



Domain of the equation: 223x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/224x-(-1/223x+30)+40=0

We get rid of parentheses

-1/224x+1/223x-30+40=0

We calculate fractions


(-223x)/49952x^2+224x/49952x^2-30+40=0

We add all the numbers together, and all the variables

(-223x)/49952x^2+224x/49952x^2+10=0

We multiply all the terms by the denominator


(-223x)+224x+10*49952x^2=0

We add all the numbers together, and all the variables

224x+(-223x)+10*49952x^2=0

Wy multiply elements

499520x^2+224x+(-223x)=0

We get rid of parentheses

499520x^2+224x-223x=0

We add all the numbers together, and all the variables

499520x^2+x=0

a = 499520; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·499520·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*499520}=\frac{-2}{999040}
=-1/499520
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*499520}=\frac{0}{999040}
=0
$