5-1/2x=3/8x-2

Solution for 5-1/2x=3/8x-2 equation:

5-1/2x=3/8x-2

We move all terms to the left:

5-1/2x-(3/8x-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

-1/2x-3/8x+2+5=0

We calculate fractions


(-8x)/16x^2+(-6x)/16x^2+2+5=0

We add all the numbers together, and all the variables

(-8x)/16x^2+(-6x)/16x^2+7=0

We multiply all the terms by the denominator


(-8x)+(-6x)+7*16x^2=0

Wy multiply elements

112x^2+(-8x)+(-6x)=0

We get rid of parentheses

112x^2-8x-6x=0

We add all the numbers together, and all the variables

112x^2-14x=0

a = 112; b = -14; c = 0;
Δ = b2-4ac
Δ = -142-4·112·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-14}{2*112}=\frac{0}{224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+14}{2*112}=\frac{28}{224}
=1/8
$