3/2x+6+1/2x=15+2x

Solution for 3/2x+6+1/2x=15+2x equation:

3/2x+6+1/2x=15+2x

We move all terms to the left:

3/2x+6+1/2x-(15+2x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/2x+1/2x-(2x+15)+6=0

We get rid of parentheses

3/2x+1/2x-2x-15+6=0

We multiply all the terms by the denominator


-2x*2x-15*2x+6*2x+3+1=0

We add all the numbers together, and all the variables

-2x*2x-15*2x+6*2x+4=0

Wy multiply elements

-4x^2-30x+12x+4=0

We add all the numbers together, and all the variables

-4x^2-18x+4=0

a = -4; b = -18; c = +4;
Δ = b2-4ac
Δ = -182-4·(-4)·4
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{97}}{2*-4}=\frac{18-2\sqrt{97}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{97}}{2*-4}=\frac{18+2\sqrt{97}}{-8}
$