9x=1/2(12x)

Solution for 9x=1/2(12x) equation:

9x=1/2(12x)

We move all terms to the left:

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


Domain of the equation: 212x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

9x-(+1/212x)=0

We get rid of parentheses

9x-1/212x=0

We multiply all the terms by the denominator


9x*212x-1=0

Wy multiply elements

1908x^2-1=0

a = 1908; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·1908·(-1)
Δ = 7632
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:

$\sqrt{\Delta}=\sqrt{7632}=\sqrt{144*53}=\sqrt{144}*\sqrt{53}=12\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{53}}{2*1908}=\frac{0-12\sqrt{53}}{3816}
=-\frac{12\sqrt{53}}{3816}
=-\frac{\sqrt{53}}{318}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{53}}{2*1908}=\frac{0+12\sqrt{53}}{3816}
=\frac{12\sqrt{53}}{3816}
=\frac{\sqrt{53}}{318}
$