5-1/2x=5/8x+16

Solution for 5-1/2x=5/8x+16 equation:

5-1/2x=5/8x+16

We move all terms to the left:

5-1/2x-(5/8x+16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+16)!=0

x∈R


We get rid of parentheses

-1/2x-5/8x-16+5=0

We calculate fractions


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

We add all the numbers together, and all the variables

(-8x)/16x^2+(-10x)/16x^2-11=0

We multiply all the terms by the denominator


(-8x)+(-10x)-11*16x^2=0

Wy multiply elements

-176x^2+(-8x)+(-10x)=0

We get rid of parentheses

-176x^2-8x-10x=0

We add all the numbers together, and all the variables

-176x^2-18x=0

a = -176; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-176)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-176}=\frac{0}{-352}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-176}=\frac{36}{-352}
=-9/88
$