2(x-6)-3=1/2x+9

Solution for 2(x-6)-3=1/2x+9 equation:

2(x-6)-3=1/2x+9

We move all terms to the left:

2(x-6)-3-(1/2x+9)=0


Domain of the equation: 2x+9)!=0

x∈R


We multiply parentheses

2x-(1/2x+9)-12-3=0

We get rid of parentheses

2x-1/2x-9-12-3=0

We multiply all the terms by the denominator


2x*2x-9*2x-12*2x-3*2x-1=0

Wy multiply elements

4x^2-18x-24x-6x-1=0

We add all the numbers together, and all the variables

4x^2-48x-1=0

a = 4; b = -48; c = -1;
Δ = b2-4ac
Δ = -482-4·4·(-1)
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{145}}{2*4}=\frac{48-4\sqrt{145}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{145}}{2*4}=\frac{48+4\sqrt{145}}{8}
$