-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-1+2))-(6(+2))=0

We add all the numbers together, and all the variables

-2x*2x+10*2x-1+2))-(62)=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{-40}{-8}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-4}=\frac{0}{-8}
=0
$