2/3x+38=8x

Solution for 2/3x+38=8x equation:

2/3x+38=8x

We move all terms to the left:

2/3x+38-(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+38=0

We multiply all the terms by the denominator


-8x*3x+38*3x+2=0

Wy multiply elements

-24x^2+114x+2=0

a = -24; b = 114; c = +2;
Δ = b2-4ac
Δ = 1142-4·(-24)·2
Δ = 13188
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:

$\sqrt{\Delta}=\sqrt{13188}=\sqrt{4*3297}=\sqrt{4}*\sqrt{3297}=2\sqrt{3297}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(114)-2\sqrt{3297}}{2*-24}=\frac{-114-2\sqrt{3297}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(114)+2\sqrt{3297}}{2*-24}=\frac{-114+2\sqrt{3297}}{-48}
$