X+x+(1/2*x)=15

Solution for X+x+(1/2*x)=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!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+X+(+1/2X)-15=0

We add all the numbers together, and all the variables

2X+(+1/2X)-15=0

We get rid of parentheses

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 = 884
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:

$\sqrt{\Delta}=\sqrt{884}=\sqrt{4*221}=\sqrt{4}*\sqrt{221}=2\sqrt{221}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{221}}{2*4}=\frac{30-2\sqrt{221}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{221}}{2*4}=\frac{30+2\sqrt{221}}{8}
$