5-1/2x=5/8x+12

Solution for 5-1/2x=5/8x+12 equation:

5-1/2x=5/8x+12

We move all terms to the left:

5-1/2x-(5/8x+12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 8x+12)!=0

x∈R


We get rid of parentheses

-1/2x-5/8x-12+5=0

We calculate fractions


(-8x)/16x^2+(-10x)/16x^2-12+5=0

We add all the numbers together, and all the variables

(-8x)/16x^2+(-10x)/16x^2-7=0

We multiply all the terms by the denominator


(-8x)+(-10x)-7*16x^2=0

Wy multiply elements

-112x^2+(-8x)+(-10x)=0

We get rid of parentheses

-112x^2-8x-10x=0

We add all the numbers together, and all the variables

-112x^2-18x=0

a = -112; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-112)·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*-112}=\frac{0}{-224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-112}=\frac{36}{-224}
=-9/56
$