1/2x-14=3/8x

Solution for 1/2x-14=3/8x equation:

1/2x-14=3/8x

We move all terms to the left:

1/2x-14-(3/8x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(+3/8x)-14=0

We get rid of parentheses

1/2x-3/8x-14=0

We calculate fractions


8x/16x^2+(-6x)/16x^2-14=0

We multiply all the terms by the denominator


8x+(-6x)-14*16x^2=0

Wy multiply elements

-224x^2+8x+(-6x)=0

We get rid of parentheses

-224x^2+8x-6x=0

We add all the numbers together, and all the variables

-224x^2+2x=0

a = -224; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-224)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-224}=\frac{-4}{-448}
=1/112
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-224}=\frac{0}{-448}
=0
$