6+8/2x=5x

Solution for 6+8/2x=5x equation:

6+8/2x=5x

We move all terms to the left:

6+8/2x-(5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-5x+8/2x+6=0

We multiply all the terms by the denominator


-5x*2x+6*2x+8=0

Wy multiply elements

-10x^2+12x+8=0

a = -10; b = 12; c = +8;
Δ = b2-4ac
Δ = 122-4·(-10)·8
Δ = 464
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:

$\sqrt{\Delta}=\sqrt{464}=\sqrt{16*29}=\sqrt{16}*\sqrt{29}=4\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{29}}{2*-10}=\frac{-12-4\sqrt{29}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{29}}{2*-10}=\frac{-12+4\sqrt{29}}{-20}
$