X+(1/2x)+(1/2x)(3)=15

Solution for X+(1/2x)+(1/2x)(3)=15 equation:

X+(1/2X)+(1/2X)(3)=15

We move all terms to the left:

X+(1/2X)+(1/2X)(3)-(15)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R



Domain of the equation: 2X)3!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+(+1/2X)+(+1/2X)3-15=0

We multiply parentheses

X+(+1/2X)+3X-15=0

We get rid of parentheses

X+1/2X+3X-15=0

We multiply all the terms by the denominator


X*2X+3X*2X-15*2X+1=0

Wy multiply elements

2X^2+6X^2-30X+1=0

We add all the numbers together, and all the variables

8X^2-30X+1=0

a = 8; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·8·1
Δ = 868
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:

$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{217}}{2*8}=\frac{30-2\sqrt{217}}{16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{217}}{2*8}=\frac{30+2\sqrt{217}}{16}
$