6/4x+1=3x+8

Solution for 6/4x+1=3x+8 equation:

6/4x+1=3x+8

We move all terms to the left:

6/4x+1-(3x+8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

6/4x-3x-8+1=0

We multiply all the terms by the denominator


-3x*4x-8*4x+1*4x+6=0

Wy multiply elements

-12x^2-32x+4x+6=0

We add all the numbers together, and all the variables

-12x^2-28x+6=0

a = -12; b = -28; c = +6;
Δ = b2-4ac
Δ = -282-4·(-12)·6
Δ = 1072
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:

$\sqrt{\Delta}=\sqrt{1072}=\sqrt{16*67}=\sqrt{16}*\sqrt{67}=4\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-4\sqrt{67}}{2*-12}=\frac{28-4\sqrt{67}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+4\sqrt{67}}{2*-12}=\frac{28+4\sqrt{67}}{-24}
$