1/2x-4=7/4x+2

Solution for 1/2x-4=7/4x+2 equation:

1/2x-4=7/4x+2

We move all terms to the left:

1/2x-4-(7/4x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



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

x∈R


We get rid of parentheses

1/2x-7/4x-2-4=0

We calculate fractions


4x/8x^2+(-14x)/8x^2-2-4=0

We add all the numbers together, and all the variables

4x/8x^2+(-14x)/8x^2-6=0

We multiply all the terms by the denominator


4x+(-14x)-6*8x^2=0

Wy multiply elements

-48x^2+4x+(-14x)=0

We get rid of parentheses

-48x^2+4x-14x=0

We add all the numbers together, and all the variables

-48x^2-10x=0

a = -48; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-48)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-48}=\frac{0}{-96}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-48}=\frac{20}{-96}
=-5/24
$