7/2x+1/2=3/16x-4

Solution for 7/2x+1/2=3/16x-4 equation:

7/2x+1/2=3/16x-4

We move all terms to the left:

7/2x+1/2-(3/16x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 16x-4)!=0

x∈R


We get rid of parentheses

7/2x-3/16x+4+1/2=0

We calculate fractions


112x/128x^2+(-24x)/128x^2+16x/128x^2+4=0

We multiply all the terms by the denominator


112x+(-24x)+16x+4*128x^2=0

We add all the numbers together, and all the variables

128x+(-24x)+4*128x^2=0

Wy multiply elements

512x^2+128x+(-24x)=0

We get rid of parentheses

512x^2+128x-24x=0

We add all the numbers together, and all the variables

512x^2+104x=0

a = 512; b = 104; c = 0;
Δ = b2-4ac
Δ = 1042-4·512·0
Δ = 10816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10816}=104$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(104)-104}{2*512}=\frac{-208}{1024}
=-13/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(104)+104}{2*512}=\frac{0}{1024}
=0
$