8x+2=3/8x+6

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

8x+2=3/8x+6

We move all terms to the left:

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


Domain of the equation: 8x+6)!=0

x∈R


We get rid of parentheses

8x-3/8x-6+2=0

We multiply all the terms by the denominator


8x*8x-6*8x+2*8x-3=0

Wy multiply elements

64x^2-48x+16x-3=0

We add all the numbers together, and all the variables

64x^2-32x-3=0

a = 64; b = -32; c = -3;
Δ = b2-4ac
Δ = -322-4·64·(-3)
Δ = 1792
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:

$\sqrt{\Delta}=\sqrt{1792}=\sqrt{256*7}=\sqrt{256}*\sqrt{7}=16\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-16\sqrt{7}}{2*64}=\frac{32-16\sqrt{7}}{128}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+16\sqrt{7}}{2*64}=\frac{32+16\sqrt{7}}{128}
$