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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


6x/8x^2+(-164x)/8x^2+2+2=0

We add all the numbers together, and all the variables

6x/8x^2+(-164x)/8x^2+4=0

We multiply all the terms by the denominator


6x+(-164x)+4*8x^2=0

Wy multiply elements

32x^2+6x+(-164x)=0

We get rid of parentheses

32x^2+6x-164x=0

We add all the numbers together, and all the variables

32x^2-158x=0

a = 32; b = -158; c = 0;
Δ = b2-4ac
Δ = -1582-4·32·0
Δ = 24964
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{24964}=158$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-158)-158}{2*32}=\frac{0}{64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-158)+158}{2*32}=\frac{316}{64}
=4+15/16
$