15-x=30/2x

Solution for 15-x=30/2x equation:

15-x=30/2x

We move all terms to the left:

15-x-(30/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-(+30/2x)+15=0

We add all the numbers together, and all the variables

-1x-(+30/2x)+15=0

We get rid of parentheses

-1x-30/2x+15=0

We multiply all the terms by the denominator


-1x*2x+15*2x-30=0

Wy multiply elements

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

a = -2; b = 30; c = -30;
Δ = b2-4ac
Δ = 302-4·(-2)·(-30)
Δ = 660
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{165}}{2*-2}=\frac{-30-2\sqrt{165}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{165}}{2*-2}=\frac{-30+2\sqrt{165}}{-4}
$