9+2x=(1/2)(18+4x)

Solution for 9+2x=(1/2)(18+4x) equation:

9+2x=(1/2)(18+4x)

We move all terms to the left:

9+2x-((1/2)(18+4x))=0


Domain of the equation: 2)(18+4x))!=0

x∈R


We add all the numbers together, and all the variables

2x-((+1/2)(4x+18))+9=0

We multiply parentheses ..

-((+4x^2+1/2*18))+2x+9=0

We multiply all the terms by the denominator


-((+4x^2+1+2x*2*18))+9*2*18))=0


We calculate terms in parentheses: -((+4x^2+1+2x*2*18)), so:

(+4x^2+1+2x*2*18)

We get rid of parentheses

4x^2+2x*2*18+1

Wy multiply elements

4x^2+72x*1+1

Wy multiply elements

4x^2+72x+1

Back to the equation:

-(4x^2+72x+1)


We add all the numbers together, and all the variables

-(4x^2+72x+1)=0

We get rid of parentheses

-4x^2-72x-1=0

a = -4; b = -72; c = -1;
Δ = b2-4ac
Δ = -722-4·(-4)·(-1)
Δ = 5168
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:

$\sqrt{\Delta}=\sqrt{5168}=\sqrt{16*323}=\sqrt{16}*\sqrt{323}=4\sqrt{323}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-4\sqrt{323}}{2*-4}=\frac{72-4\sqrt{323}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+4\sqrt{323}}{2*-4}=\frac{72+4\sqrt{323}}{-8}
$