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

Solution for 2(x-2)=(2/7)(x+4) equation:

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

We move all terms to the left:

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


Domain of the equation: 7)(x+4))!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


-((+2x^2+2+2x*7*4))-4*7*4))=0


We calculate terms in parentheses: -((+2x^2+2+2x*7*4)), so:

(+2x^2+2+2x*7*4)

We get rid of parentheses

2x^2+2x*7*4+2

Wy multiply elements

2x^2+56x*4+2

Wy multiply elements

2x^2+224x+2

Back to the equation:

-(2x^2+224x+2)


We add all the numbers together, and all the variables

-(2x^2+224x+2)=0

We get rid of parentheses

-2x^2-224x-2=0

a = -2; b = -224; c = -2;
Δ = b2-4ac
Δ = -2242-4·(-2)·(-2)
Δ = 50160
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:

$\sqrt{\Delta}=\sqrt{50160}=\sqrt{16*3135}=\sqrt{16}*\sqrt{3135}=4\sqrt{3135}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-4\sqrt{3135}}{2*-2}=\frac{224-4\sqrt{3135}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+4\sqrt{3135}}{2*-2}=\frac{224+4\sqrt{3135}}{-4}
$