8x-16=58/6x

Solution for 8x-16=58/6x equation:

8x-16=58/6x

We move all terms to the left:

8x-16-(58/6x)=0


Domain of the equation: 6x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

8x-(+58/6x)-16=0

We get rid of parentheses

8x-58/6x-16=0

We multiply all the terms by the denominator


8x*6x-16*6x-58=0

Wy multiply elements

48x^2-96x-58=0

a = 48; b = -96; c = -58;
Δ = b2-4ac
Δ = -962-4·48·(-58)
Δ = 20352
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:

$\sqrt{\Delta}=\sqrt{20352}=\sqrt{64*318}=\sqrt{64}*\sqrt{318}=8\sqrt{318}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-96)-8\sqrt{318}}{2*48}=\frac{96-8\sqrt{318}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-96)+8\sqrt{318}}{2*48}=\frac{96+8\sqrt{318}}{96}
$