3/8x-1/21x+8/21=17/24

Solution for 3/8x-1/21x+8/21=17/24 equation:

3/8x-1/21x+8/21=17/24

We move all terms to the left:

3/8x-1/21x+8/21-(17/24)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 21x!=0

x!=0/21

x!=0

x∈R


We add all the numbers together, and all the variables

3/8x-1/21x+8/21-(+17/24)=0

We get rid of parentheses

3/8x-1/21x+8/21-17/24=0

We calculate fractions


(-119952x^2)/169344x^2+63504x/169344x^2+(-384x)/169344x^2+3072x/169344x^2=0

We multiply all the terms by the denominator


(-119952x^2)+63504x+(-384x)+3072x=0

We add all the numbers together, and all the variables

(-119952x^2)+66576x+(-384x)=0

We get rid of parentheses

-119952x^2+66576x-384x=0

We add all the numbers together, and all the variables

-119952x^2+66192x=0

a = -119952; b = 66192; c = 0;
Δ = b2-4ac
Δ = 661922-4·(-119952)·0
Δ = 4381380864
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4381380864}=66192$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66192)-66192}{2*-119952}=\frac{-132384}{-239904}
=197/357
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66192)+66192}{2*-119952}=\frac{0}{-239904}
=0
$