x+x-1/2x=15

Solution for x+x-1/2x=15 equation:

x+x-1/2x=15

We move all terms to the left:

x+x-1/2x-(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

2x-1/2x-15=0

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2-30x-1=0

a = 4; b = -30; c = -1;
Δ = b2-4ac
Δ = -302-4·4·(-1)
Δ = 916
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:

$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{229}}{2*4}=\frac{30-2\sqrt{229}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{229}}{2*4}=\frac{30+2\sqrt{229}}{8}
$