1/2x-(3/4x+2)=1/2x-5

Solution for 1/2x-(3/4x+2)=1/2x-5 equation:

1/2x-(3/4x+2)=1/2x-5

We move all terms to the left:

1/2x-(3/4x+2)-(1/2x-5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+2)!=0

x∈R



Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

1/2x-3/4x-1/2x-2+5=0

We calculate fractions


(-4x+1)/8x^2+(-6x)/8x^2-2+5=0

We add all the numbers together, and all the variables

(-4x+1)/8x^2+(-6x)/8x^2+3=0

We multiply all the terms by the denominator


(-4x+1)+(-6x)+3*8x^2=0

Wy multiply elements

24x^2+(-4x+1)+(-6x)=0

We get rid of parentheses

24x^2-4x-6x+1=0

We add all the numbers together, and all the variables

24x^2-10x+1=0

a = 24; b = -10; c = +1;
Δ = b2-4ac
Δ = -102-4·24·1
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*24}=\frac{8}{48}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*24}=\frac{12}{48}
=1/4
$