4x+8/2x=46

Solution for 4x+8/2x=46 equation:

4x+8/2x=46

We move all terms to the left:

4x+8/2x-(46)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-46*2x+8=0

Wy multiply elements

8x^2-92x+8=0

a = 8; b = -92; c = +8;
Δ = b2-4ac
Δ = -922-4·8·8
Δ = 8208
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:

$\sqrt{\Delta}=\sqrt{8208}=\sqrt{144*57}=\sqrt{144}*\sqrt{57}=12\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-12\sqrt{57}}{2*8}=\frac{92-12\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+12\sqrt{57}}{2*8}=\frac{92+12\sqrt{57}}{16}
$