x/2x-4x-3=27.

Solution for x/2x-4x-3=27. equation:

x/2x-4x-3=27.

We move all terms to the left:

x/2x-4x-3-(27.)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

x/2x-4x-3-27=0

We add all the numbers together, and all the variables

-4x+x/2x-30=0

We multiply all the terms by the denominator


-4x*2x+x-30*2x=0

We add all the numbers together, and all the variables

x-4x*2x-30*2x=0

Wy multiply elements

-8x^2+x-60x=0

We add all the numbers together, and all the variables

-8x^2-59x=0

a = -8; b = -59; c = 0;
Δ = b2-4ac
Δ = -592-4·(-8)·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59)-59}{2*-8}=\frac{0}{-16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59)+59}{2*-8}=\frac{118}{-16}
=-7+3/8
$