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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x+7/2x+4x-28=0

We multiply all the terms by the denominator


-2x*2x+4x*2x-28*2x+7=0

Wy multiply elements

-4x^2+8x^2-56x+7=0

We add all the numbers together, and all the variables

4x^2-56x+7=0

a = 4; b = -56; c = +7;
Δ = b2-4ac
Δ = -562-4·4·7
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-12\sqrt{21}}{2*4}=\frac{56-12\sqrt{21}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+12\sqrt{21}}{2*4}=\frac{56+12\sqrt{21}}{8}
$