2/3x-1/3x+11=8x=

Solution for 2/3x-1/3x+11=8x= equation:

2/3x-1/3x+11=8x=

We move all terms to the left:

2/3x-1/3x+11-(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

-8x+2/3x-1/3x+11=0

We multiply all the terms by the denominator


-8x*3x+11*3x+2-1=0

We add all the numbers together, and all the variables

-8x*3x+11*3x+1=0

Wy multiply elements

-24x^2+33x+1=0

a = -24; b = 33; c = +1;
Δ = b2-4ac
Δ = 332-4·(-24)·1
Δ = 1185
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{-(33)-\sqrt{1185}}{2*-24}=\frac{-33-\sqrt{1185}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1185}}{2*-24}=\frac{-33+\sqrt{1185}}{-48}
$