41/2-3/4x=3-1/2x

Solution for 41/2-3/4x=3-1/2x equation:

41/2-3/4x=3-1/2x

We move all terms to the left:

41/2-3/4x-(3-1/2x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-3/4x-(-1/2x+3)+41/2=0

We get rid of parentheses

-3/4x+1/2x-3+41/2=0

We calculate fractions


(-24x)/32x^2+4x/32x^2+164x/32x^2-3=0

We multiply all the terms by the denominator


(-24x)+4x+164x-3*32x^2=0

We add all the numbers together, and all the variables

168x+(-24x)-3*32x^2=0

Wy multiply elements

-96x^2+168x+(-24x)=0

We get rid of parentheses

-96x^2+168x-24x=0

We add all the numbers together, and all the variables

-96x^2+144x=0

a = -96; b = 144; c = 0;
Δ = b2-4ac
Δ = 1442-4·(-96)·0
Δ = 20736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{20736}=144$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-144}{2*-96}=\frac{-288}{-192}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+144}{2*-96}=\frac{0}{-192}
=0
$