4x-32=58/2x

Solution for 4x-32=58/2x equation:

4x-32=58/2x

We move all terms to the left:

4x-32-(58/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x-(+58/2x)-32=0

We get rid of parentheses

4x-58/2x-32=0

We multiply all the terms by the denominator


4x*2x-32*2x-58=0

Wy multiply elements

8x^2-64x-58=0

a = 8; b = -64; c = -58;
Δ = b2-4ac
Δ = -642-4·8·(-58)
Δ = 5952
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:

$\sqrt{\Delta}=\sqrt{5952}=\sqrt{64*93}=\sqrt{64}*\sqrt{93}=8\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{93}}{2*8}=\frac{64-8\sqrt{93}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{93}}{2*8}=\frac{64+8\sqrt{93}}{16}
$