6x+2=3/8x-4

Solution for 6x+2=3/8x-4 equation:

6x+2=3/8x-4

We move all terms to the left:

6x+2-(3/8x-4)=0


Domain of the equation: 8x-4)!=0

x∈R


We get rid of parentheses

6x-3/8x+4+2=0

We multiply all the terms by the denominator


6x*8x+4*8x+2*8x-3=0

Wy multiply elements

48x^2+32x+16x-3=0

We add all the numbers together, and all the variables

48x^2+48x-3=0

a = 48; b = 48; c = -3;
Δ = b2-4ac
Δ = 482-4·48·(-3)
Δ = 2880
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:

$\sqrt{\Delta}=\sqrt{2880}=\sqrt{576*5}=\sqrt{576}*\sqrt{5}=24\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-24\sqrt{5}}{2*48}=\frac{-48-24\sqrt{5}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+24\sqrt{5}}{2*48}=\frac{-48+24\sqrt{5}}{96}
$