1/2x+3/8=7/8x+43

Solution for 1/2x+3/8=7/8x+43 equation:

1/2x+3/8=7/8x+43

We move all terms to the left:

1/2x+3/8-(7/8x+43)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+43)!=0

x∈R


We get rid of parentheses

1/2x-7/8x-43+3/8=0

We calculate fractions


512x/1024x^2+(-14x)/1024x^2+6x/1024x^2-43=0

We multiply all the terms by the denominator


512x+(-14x)+6x-43*1024x^2=0

We add all the numbers together, and all the variables

518x+(-14x)-43*1024x^2=0

Wy multiply elements

-44032x^2+518x+(-14x)=0

We get rid of parentheses

-44032x^2+518x-14x=0

We add all the numbers together, and all the variables

-44032x^2+504x=0

a = -44032; b = 504; c = 0;
Δ = b2-4ac
Δ = 5042-4·(-44032)·0
Δ = 254016
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{254016}=504$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(504)-504}{2*-44032}=\frac{-1008}{-88064}
=63/5504
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(504)+504}{2*-44032}=\frac{0}{-88064}
=0
$