3/4x+6=x+2

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

3/4x+6=x+2

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-8x+24x+3=0

We add all the numbers together, and all the variables

-4x^2+16x+3=0

a = -4; b = 16; c = +3;
Δ = b2-4ac
Δ = 162-4·(-4)·3
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{19}}{2*-4}=\frac{-16-4\sqrt{19}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{19}}{2*-4}=\frac{-16+4\sqrt{19}}{-8}
$