x/2x-32x=15

Solution for x/2x-32x=15 equation:

x/2x-32x=15

We move all terms to the left:

x/2x-32x-(15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-32x+x/2x-15=0

We multiply all the terms by the denominator


-32x*2x+x-15*2x=0

We add all the numbers together, and all the variables

x-32x*2x-15*2x=0

Wy multiply elements

-64x^2+x-30x=0

We add all the numbers together, and all the variables

-64x^2-29x=0

a = -64; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·(-64)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*-64}=\frac{0}{-128}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*-64}=\frac{58}{-128}
=-29/64
$