7/2x+2=4+7x

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

7/2x+2=4+7x

We move all terms to the left:

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-14x^2-8x+4x+7=0

We add all the numbers together, and all the variables

-14x^2-4x+7=0

a = -14; b = -4; c = +7;
Δ = b2-4ac
Δ = -42-4·(-14)·7
Δ = 408
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:

$\sqrt{\Delta}=\sqrt{408}=\sqrt{4*102}=\sqrt{4}*\sqrt{102}=2\sqrt{102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{102}}{2*-14}=\frac{4-2\sqrt{102}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{102}}{2*-14}=\frac{4+2\sqrt{102}}{-28}
$