6/8x+2=4x-8

Solution for 6/8x+2=4x-8 equation:

6/8x+2=4x-8

We move all terms to the left:

6/8x+2-(4x-8)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We get rid of parentheses

6/8x-4x+8+2=0

We multiply all the terms by the denominator


-4x*8x+8*8x+2*8x+6=0

Wy multiply elements

-32x^2+64x+16x+6=0

We add all the numbers together, and all the variables

-32x^2+80x+6=0

a = -32; b = 80; c = +6;
Δ = b2-4ac
Δ = 802-4·(-32)·6
Δ = 7168
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:

$\sqrt{\Delta}=\sqrt{7168}=\sqrt{1024*7}=\sqrt{1024}*\sqrt{7}=32\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-32\sqrt{7}}{2*-32}=\frac{-80-32\sqrt{7}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+32\sqrt{7}}{2*-32}=\frac{-80+32\sqrt{7}}{-64}
$