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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


8x/16x^2+(-10x)/16x^2-4+5=0

We add all the numbers together, and all the variables

8x/16x^2+(-10x)/16x^2+1=0

We multiply all the terms by the denominator


8x+(-10x)+1*16x^2=0

Wy multiply elements

16x^2+8x+(-10x)=0

We get rid of parentheses

16x^2+8x-10x=0

We add all the numbers together, and all the variables

16x^2-2x=0

a = 16; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·16·0
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*16}=\frac{0}{32}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2}{2*16}=\frac{4}{32}
=1/8
$