24-1/20(3x)=16-1/20(2x)

Solution for 24-1/20(3x)=16-1/20(2x) equation:

24-1/20(3x)=16-1/20(2x)

We move all terms to the left:

24-1/20(3x)-(16-1/20(2x))=0


Domain of the equation: 203x!=0

x!=0/203

x!=0

x∈R



Domain of the equation: 202x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-1/203x-(-1/202x+16)+24=0

We get rid of parentheses

-1/203x+1/202x-16+24=0

We calculate fractions


(-202x)/41006x^2+203x/41006x^2-16+24=0

We add all the numbers together, and all the variables

(-202x)/41006x^2+203x/41006x^2+8=0

We multiply all the terms by the denominator


(-202x)+203x+8*41006x^2=0

We add all the numbers together, and all the variables

203x+(-202x)+8*41006x^2=0

Wy multiply elements

328048x^2+203x+(-202x)=0

We get rid of parentheses

328048x^2+203x-202x=0

We add all the numbers together, and all the variables

328048x^2+x=0

a = 328048; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·328048·0
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*328048}=\frac{-2}{656096}
=-1/328048
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*328048}=\frac{0}{656096}
=0
$