21-9(8-6x)=22/8*x

Solution for 21-9(8-6x)=22/8*x equation:

21-9(8-6x)=22/8x

We move all terms to the left:

21-9(8-6x)-(22/8x)=0


Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-9(-6x+8)-(+22/8x)+21=0

We multiply parentheses

54x-(+22/8x)-72+21=0

We get rid of parentheses

54x-22/8x-72+21=0

We multiply all the terms by the denominator


54x*8x-72*8x+21*8x-22=0

Wy multiply elements

432x^2-576x+168x-22=0

We add all the numbers together, and all the variables

432x^2-408x-22=0

a = 432; b = -408; c = -22;
Δ = b2-4ac
Δ = -4082-4·432·(-22)
Δ = 204480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{204480}=\sqrt{576*355}=\sqrt{576}*\sqrt{355}=24\sqrt{355}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-408)-24\sqrt{355}}{2*432}=\frac{408-24\sqrt{355}}{864}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-408)+24\sqrt{355}}{2*432}=\frac{408+24\sqrt{355}}{864}
$