16-1/2x=3/8x+1

Solution for 16-1/2x=3/8x+1 equation:

16-1/2x=3/8x+1

We move all terms to the left:

16-1/2x-(3/8x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+1)!=0

x∈R


We get rid of parentheses

-1/2x-3/8x-1+16=0

We calculate fractions


(-8x)/16x^2+(-6x)/16x^2-1+16=0

We add all the numbers together, and all the variables

(-8x)/16x^2+(-6x)/16x^2+15=0

We multiply all the terms by the denominator


(-8x)+(-6x)+15*16x^2=0

Wy multiply elements

240x^2+(-8x)+(-6x)=0

We get rid of parentheses

240x^2-8x-6x=0

We add all the numbers together, and all the variables

240x^2-14x=0

a = 240; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·240·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*240}=\frac{0}{480}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*240}=\frac{28}{480}
=7/120
$