x=3/8x+9-6x

Solution for x=3/8x+9-6x equation:

x=3/8x+9-6x

We move all terms to the left:

x-(3/8x+9-6x)=0


Domain of the equation: 8x+9-6x)!=0

We move all terms containing x to the left, all other terms to the right

8x-6x)!=-9

x∈R


We add all the numbers together, and all the variables

x-(-6x+3/8x+9)=0

We get rid of parentheses

x+6x-3/8x-9=0

We multiply all the terms by the denominator


x*8x+6x*8x-9*8x-3=0

Wy multiply elements

8x^2+48x^2-72x-3=0

We add all the numbers together, and all the variables

56x^2-72x-3=0

a = 56; b = -72; c = -3;
Δ = b2-4ac
Δ = -722-4·56·(-3)
Δ = 5856
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:

$\sqrt{\Delta}=\sqrt{5856}=\sqrt{16*366}=\sqrt{16}*\sqrt{366}=4\sqrt{366}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{366}}{2*56}=\frac{72-4\sqrt{366}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{366}}{2*56}=\frac{72+4\sqrt{366}}{112}
$