6/4x+1=x+4

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

6/4x+1=x+4

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-16x+4x+6=0

We add all the numbers together, and all the variables

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

a = -4; b = -12; c = +6;
Δ = b2-4ac
Δ = -122-4·(-4)·6
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{15}}{2*-4}=\frac{12-4\sqrt{15}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{15}}{2*-4}=\frac{12+4\sqrt{15}}{-8}
$