4x+2=1/24x+44

Solution for 4x+2=1/24x+44 equation:

4x+2=1/24x+44

We move all terms to the left:

4x+2-(1/24x+44)=0


Domain of the equation: 24x+44)!=0

x∈R


We get rid of parentheses

4x-1/24x-44+2=0

We multiply all the terms by the denominator


4x*24x-44*24x+2*24x-1=0

Wy multiply elements

96x^2-1056x+48x-1=0

We add all the numbers together, and all the variables

96x^2-1008x-1=0

a = 96; b = -1008; c = -1;
Δ = b2-4ac
Δ = -10082-4·96·(-1)
Δ = 1016448
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:

$\sqrt{\Delta}=\sqrt{1016448}=\sqrt{64*15882}=\sqrt{64}*\sqrt{15882}=8\sqrt{15882}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1008)-8\sqrt{15882}}{2*96}=\frac{1008-8\sqrt{15882}}{192}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1008)+8\sqrt{15882}}{2*96}=\frac{1008+8\sqrt{15882}}{192}
$