7/2x-2+1/2x=28+4x

Solution for 7/2x-2+1/2x=28+4x equation:

7/2x-2+1/2x=28+4x

We move all terms to the left:

7/2x-2+1/2x-(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+1/2x-(4x+28)-2=0

We get rid of parentheses

7/2x+1/2x-4x-28-2=0

We multiply all the terms by the denominator


-4x*2x-28*2x-2*2x+7+1=0

We add all the numbers together, and all the variables

-4x*2x-28*2x-2*2x+8=0

Wy multiply elements

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

We add all the numbers together, and all the variables

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

a = -8; b = -60; c = +8;
Δ = b2-4ac
Δ = -602-4·(-8)·8
Δ = 3856
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:

$\sqrt{\Delta}=\sqrt{3856}=\sqrt{16*241}=\sqrt{16}*\sqrt{241}=4\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{241}}{2*-8}=\frac{60-4\sqrt{241}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{241}}{2*-8}=\frac{60+4\sqrt{241}}{-16}
$