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

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

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

We move all terms to the left:

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


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R



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

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4(+1/2x)-(42-4(+3/4x))-43=0

We multiply parentheses

4x-(42-4(+3/4x))-43=0

We multiply all the terms by the denominator


4x*4x))-(42-4(-43*4x))+3=0

Wy multiply elements

16x^2-172x=0

a = 16; b = -172; c = 0;
Δ = b2-4ac
Δ = -1722-4·16·0
Δ = 29584
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{29584}=172$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-172)-172}{2*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-172)+172}{2*16}=\frac{344}{32}
=10+3/4
$