-32/8x+224/21x=51/12

Solution for -32/8x+224/21x=51/12 equation:

-32/8x+224/21x=51/12

We move all terms to the left:

-32/8x+224/21x-(51/12)=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

-32/8x+224/21x-(+51/12)=0

We get rid of parentheses

-32/8x+224/21x-51/12=0

We calculate fractions


(-17136x^2)/2016x^2+(-8064x)/2016x^2+21504x/2016x^2=0

We multiply all the terms by the denominator


(-17136x^2)+(-8064x)+21504x=0

We add all the numbers together, and all the variables

(-17136x^2)+21504x+(-8064x)=0

We get rid of parentheses

-17136x^2+21504x-8064x=0

We add all the numbers together, and all the variables

-17136x^2+13440x=0

a = -17136; b = 13440; c = 0;
Δ = b2-4ac
Δ = 134402-4·(-17136)·0
Δ = 180633600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{180633600}=13440$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13440)-13440}{2*-17136}=\frac{-26880}{-34272}
=40/51
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13440)+13440}{2*-17136}=\frac{0}{-34272}
=0
$