5(x-2)=4(1/2x+2)

Solution for 5(x-2)=4(1/2x+2) equation:

5(x-2)=4(1/2x+2)

We move all terms to the left:

5(x-2)-(4(1/2x+2))=0


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

x∈R


We multiply parentheses

5x-(4(1/2x+2))-10=0

We multiply all the terms by the denominator


5x*2x-10*2x+2))-(4(1+2))=0

We add all the numbers together, and all the variables

5x*2x-10*2x+2))-(43)=0

We add all the numbers together, and all the variables

5x*2x-10*2x=0

Wy multiply elements

10x^2-20x=0

a = 10; b = -20; c = 0;
Δ = b2-4ac
Δ = -202-4·10·0
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*10}=\frac{0}{20}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20}{2*10}=\frac{40}{20}
=2
$