1/2x-3/8x+8=1/4

Solution for 1/2x-3/8x+8=1/4 equation:

1/2x-3/8x+8=1/4

We move all terms to the left:

1/2x-3/8x+8-(1/4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-3/8x+8-(+1/4)=0

We get rid of parentheses

1/2x-3/8x+8-1/4=0

We calculate fractions


(-128x^2)/256x^2+128x/256x^2+(-96x)/256x^2+8=0

We multiply all the terms by the denominator


(-128x^2)+128x+(-96x)+8*256x^2=0

Wy multiply elements

(-128x^2)+2048x^2+128x+(-96x)=0

We get rid of parentheses

-128x^2+2048x^2+128x-96x=0

We add all the numbers together, and all the variables

1920x^2+32x=0

a = 1920; b = 32; c = 0;
Δ = b2-4ac
Δ = 322-4·1920·0
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-32}{2*1920}=\frac{-64}{3840}
=-1/60
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+32}{2*1920}=\frac{0}{3840}
=0
$