5/8x-3/4x+4=1/2

Solution for 5/8x-3/4x+4=1/2 equation:

5/8x-3/4x+4=1/2

We move all terms to the left:

5/8x-3/4x+4-(1/2)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5/8x-3/4x+4-(+1/2)=0

We get rid of parentheses

5/8x-3/4x+4-1/2=0

We calculate fractions


(-128x^2)/128x^2+80x/128x^2+(-96x)/128x^2+4=0

We multiply all the terms by the denominator


(-128x^2)+80x+(-96x)+4*128x^2=0

Wy multiply elements

(-128x^2)+512x^2+80x+(-96x)=0

We get rid of parentheses

-128x^2+512x^2+80x-96x=0

We add all the numbers together, and all the variables

384x^2-16x=0

a = 384; b = -16; c = 0;
Δ = b2-4ac
Δ = -162-4·384·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-16}{2*384}=\frac{0}{768}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+16}{2*384}=\frac{32}{768}
=1/24
$