7/2x+1/2x=2x+12/2=7/2x

Solution for 7/2x+1/2x=2x+12/2=7/2x equation:

7/2x+1/2x=2x+12/2=7/2x

We move all terms to the left:

7/2x+1/2x-(2x+12/2)=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-(2x+6)=0

We get rid of parentheses

7/2x+1/2x-2x-6=0

We multiply all the terms by the denominator


-2x*2x-6*2x+7+1=0

We add all the numbers together, and all the variables

-2x*2x-6*2x+8=0

Wy multiply elements

-4x^2-12x+8=0

a = -4; b = -12; c = +8;
Δ = b2-4ac
Δ = -122-4·(-4)·8
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{17}}{2*-4}=\frac{12-4\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{17}}{2*-4}=\frac{12+4\sqrt{17}}{-8}
$