4x+2=31/4x+6

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

4x+2=31/4x+6

We move all terms to the left:

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


Domain of the equation: 4x+6)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

16x^2-24x+8x-31=0

We add all the numbers together, and all the variables

16x^2-16x-31=0

a = 16; b = -16; c = -31;
Δ = b2-4ac
Δ = -162-4·16·(-31)
Δ = 2240
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:

$\sqrt{\Delta}=\sqrt{2240}=\sqrt{64*35}=\sqrt{64}*\sqrt{35}=8\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8\sqrt{35}}{2*16}=\frac{16-8\sqrt{35}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8\sqrt{35}}{2*16}=\frac{16+8\sqrt{35}}{32}
$