4x+2=31/2x+6

Solution for 4x+2=31/2x+6 equation:

4x+2=31/2x+6

We move all terms to the left:

4x+2-(31/2x+6)=0


Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

4x-31/2x-6+2=0

We multiply all the terms by the denominator


4x*2x-6*2x+2*2x-31=0

Wy multiply elements

8x^2-12x+4x-31=0

We add all the numbers together, and all the variables

8x^2-8x-31=0

a = 8; b = -8; c = -31;
Δ = b2-4ac
Δ = -82-4·8·(-31)
Δ = 1056
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:

$\sqrt{\Delta}=\sqrt{1056}=\sqrt{16*66}=\sqrt{16}*\sqrt{66}=4\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{66}}{2*8}=\frac{8-4\sqrt{66}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{66}}{2*8}=\frac{8+4\sqrt{66}}{16}
$