(3x-2x*3)-1/2x=5

Solution for (3x-2x*3)-1/2x=5 equation:

(3x-2x*3)-1/2x=5

We move all terms to the left:

(3x-2x*3)-1/2x-(5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

3x-2x*3-1/2x-5=0

We multiply all the terms by the denominator


3x*2x-(2x*3)*2x-5*2x-1=0

We add all the numbers together, and all the variables

3x*2x-(+2x*3)*2x-5*2x-1=0

We multiply parentheses

-12x^2+3x*2x-5*2x-1=0

Wy multiply elements

-12x^2+6x^2-10x-1=0

We add all the numbers together, and all the variables

-6x^2-10x-1=0

a = -6; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·(-6)·(-1)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{19}}{2*-6}=\frac{10-2\sqrt{19}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{19}}{2*-6}=\frac{10+2\sqrt{19}}{-12}
$