8x=2/39x+6

Solution for 8x=2/39x+6 equation:

8x=2/39x+6

We move all terms to the left:

8x-(2/39x+6)=0


Domain of the equation: 39x+6)!=0

x∈R


We get rid of parentheses

8x-2/39x-6=0

We multiply all the terms by the denominator


8x*39x-6*39x-2=0

Wy multiply elements

312x^2-234x-2=0

a = 312; b = -234; c = -2;
Δ = b2-4ac
Δ = -2342-4·312·(-2)
Δ = 57252
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:

$\sqrt{\Delta}=\sqrt{57252}=\sqrt{4*14313}=\sqrt{4}*\sqrt{14313}=2\sqrt{14313}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-234)-2\sqrt{14313}}{2*312}=\frac{234-2\sqrt{14313}}{624}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-234)+2\sqrt{14313}}{2*312}=\frac{234+2\sqrt{14313}}{624}
$