6x-2=1/2x+9

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

6x-2=1/2x+9

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

6x-1/2x-9-2=0

We multiply all the terms by the denominator


6x*2x-9*2x-2*2x-1=0

Wy multiply elements

12x^2-18x-4x-1=0

We add all the numbers together, and all the variables

12x^2-22x-1=0

a = 12; b = -22; c = -1;
Δ = b2-4ac
Δ = -222-4·12·(-1)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{133}}{2*12}=\frac{22-2\sqrt{133}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{133}}{2*12}=\frac{22+2\sqrt{133}}{24}
$