9x+6=2/3(8x)

Solution for 9x+6=2/3(8x) equation:

9x+6=2/3(8x)

We move all terms to the left:

9x+6-(2/3(8x))=0


Domain of the equation: 38x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x-(+2/38x)+6=0

We get rid of parentheses

9x-2/38x+6=0

We multiply all the terms by the denominator


9x*38x+6*38x-2=0

Wy multiply elements

342x^2+228x-2=0

a = 342; b = 228; c = -2;
Δ = b2-4ac
Δ = 2282-4·342·(-2)
Δ = 54720
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:

$\sqrt{\Delta}=\sqrt{54720}=\sqrt{576*95}=\sqrt{576}*\sqrt{95}=24\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(228)-24\sqrt{95}}{2*342}=\frac{-228-24\sqrt{95}}{684}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(228)+24\sqrt{95}}{2*342}=\frac{-228+24\sqrt{95}}{684}
$