32/3x+20=171-8x

Solution for 32/3x+20=171-8x equation:

32/3x+20=171-8x

We move all terms to the left:

32/3x+20-(171-8x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

32/3x-(-8x+171)+20=0

We get rid of parentheses

32/3x+8x-171+20=0

We multiply all the terms by the denominator


8x*3x-171*3x+20*3x+32=0

Wy multiply elements

24x^2-513x+60x+32=0

We add all the numbers together, and all the variables

24x^2-453x+32=0

a = 24; b = -453; c = +32;
Δ = b2-4ac
Δ = -4532-4·24·32
Δ = 202137
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-453)-\sqrt{202137}}{2*24}=\frac{453-\sqrt{202137}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-453)+\sqrt{202137}}{2*24}=\frac{453+\sqrt{202137}}{48}
$