7/2x-2=28x-4x

Solution for 7/2x-2=28x-4x equation:

7/2x-2=28x-4x

We move all terms to the left:

7/2x-2-(28x-4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x-(+24x)-2=0

We get rid of parentheses

7/2x-24x-2=0

We multiply all the terms by the denominator


-24x*2x-2*2x+7=0

Wy multiply elements

-48x^2-4x+7=0

a = -48; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-48)·7
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{85}}{2*-48}=\frac{4-4\sqrt{85}}{-96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{85}}{2*-48}=\frac{4+4\sqrt{85}}{-96}
$