2(x-5)=6(2+1/2x)

Solution for 2(x-5)=6(2+1/2x) equation:

2(x-5)=6(2+1/2x)

We move all terms to the left:

2(x-5)-(6(2+1/2x))=0


Domain of the equation: 2x))!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2(x-5)-(6(1/2x+2))=0

We multiply parentheses

2x-(6(1/2x+2))-10=0

We multiply all the terms by the denominator


2x*2x-10*2x+2))-(6(1+2))=0

We add all the numbers together, and all the variables

2x*2x-10*2x+2))-(63)=0

We add all the numbers together, and all the variables

2x*2x-10*2x=0

Wy multiply elements

4x^2-20x=0

a = 4; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·4·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*4}=\frac{40}{8}
=5
$