7/2x+2=28+4x

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

7/2x+2=28+4x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-8x^2-52x+7=0

a = -8; b = -52; c = +7;
Δ = b2-4ac
Δ = -522-4·(-8)·7
Δ = 2928
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:

$\sqrt{\Delta}=\sqrt{2928}=\sqrt{16*183}=\sqrt{16}*\sqrt{183}=4\sqrt{183}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{183}}{2*-8}=\frac{52-4\sqrt{183}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{183}}{2*-8}=\frac{52+4\sqrt{183}}{-16}
$