-51/2x=5/8x+2

Solution for -51/2x=5/8x+2 equation:

-51/2x=5/8x+2

We move all terms to the left:

-51/2x-(5/8x+2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+2)!=0

x∈R


We get rid of parentheses

-51/2x-5/8x-2=0

We calculate fractions


(-408x)/16x^2+(-10x)/16x^2-2=0

We multiply all the terms by the denominator


(-408x)+(-10x)-2*16x^2=0

Wy multiply elements

-32x^2+(-408x)+(-10x)=0

We get rid of parentheses

-32x^2-408x-10x=0

We add all the numbers together, and all the variables

-32x^2-418x=0

a = -32; b = -418; c = 0;
Δ = b2-4ac
Δ = -4182-4·(-32)·0
Δ = 174724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{174724}=418$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-418)-418}{2*-32}=\frac{0}{-64}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-418)+418}{2*-32}=\frac{836}{-64}
=-13+1/16
$