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

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

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

We move all terms to the left:

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


Domain of the equation: 22x!=0

x!=0/22

x!=0

x∈R



Domain of the equation: 45x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/22x-(+1/45x)-2=0

We get rid of parentheses

1/22x-1/45x-2=0

We calculate fractions


45x/990x^2+(-22x)/990x^2-2=0

We multiply all the terms by the denominator


45x+(-22x)-2*990x^2=0

Wy multiply elements

-1980x^2+45x+(-22x)=0

We get rid of parentheses

-1980x^2+45x-22x=0

We add all the numbers together, and all the variables

-1980x^2+23x=0

a = -1980; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-1980)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-1980}=\frac{-46}{-3960}
=23/1980
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-1980}=\frac{0}{-3960}
=0
$