3/2x-x+5=x+9

Solution for 3/2x-x+5=x+9 equation:

3/2x-x+5=x+9

We move all terms to the left:

3/2x-x+5-(x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+3/2x-(x+9)+5=0

We get rid of parentheses

-1x+3/2x-x-9+5=0

We multiply all the terms by the denominator


-1x*2x-x*2x-9*2x+5*2x+3=0

Wy multiply elements

-2x^2-2x^2-18x+10x+3=0

We add all the numbers together, and all the variables

-4x^2-8x+3=0

a = -4; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·(-4)·3
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*-4}=\frac{8-4\sqrt{7}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*-4}=\frac{8+4\sqrt{7}}{-8}
$