6(x)=1/2x+9

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

6(x)=1/2x+9

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

6x-1/2x-9=0

We multiply all the terms by the denominator


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

Wy multiply elements

12x^2-18x-1=0

a = 12; b = -18; c = -1;
Δ = b2-4ac
Δ = -182-4·12·(-1)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{93}}{2*12}=\frac{18-2\sqrt{93}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{93}}{2*12}=\frac{18+2\sqrt{93}}{24}
$