6x-5/2x=28

Solution for 6x-5/2x=28 equation:

6x-5/2x=28

We move all terms to the left:

6x-5/2x-(28)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


6x*2x-28*2x-5=0

Wy multiply elements

12x^2-56x-5=0

a = 12; b = -56; c = -5;
Δ = b2-4ac
Δ = -562-4·12·(-5)
Δ = 3376
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:

$\sqrt{\Delta}=\sqrt{3376}=\sqrt{16*211}=\sqrt{16}*\sqrt{211}=4\sqrt{211}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{211}}{2*12}=\frac{56-4\sqrt{211}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{211}}{2*12}=\frac{56+4\sqrt{211}}{24}
$