x/8x+6+3x-2=37

Solution for x/8x+6+3x-2=37 equation:

x/8x+6+3x-2=37

We move all terms to the left:

x/8x+6+3x-2-(37)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

3x+x/8x-33=0

We multiply all the terms by the denominator


3x*8x+x-33*8x=0

We add all the numbers together, and all the variables

x+3x*8x-33*8x=0

Wy multiply elements

24x^2+x-264x=0

We add all the numbers together, and all the variables

24x^2-263x=0

a = 24; b = -263; c = 0;
Δ = b2-4ac
Δ = -2632-4·24·0
Δ = 69169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{69169}=263$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-263)-263}{2*24}=\frac{0}{48}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-263)+263}{2*24}=\frac{526}{48}
=10+23/24
$