x-9/2x=12

Solution for x-9/2x=12 equation:

x-9/2x=12

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

2x^2-24x-9=0

a = 2; b = -24; c = -9;
Δ = b2-4ac
Δ = -242-4·2·(-9)
Δ = 648
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:

$\sqrt{\Delta}=\sqrt{648}=\sqrt{324*2}=\sqrt{324}*\sqrt{2}=18\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18\sqrt{2}}{2*2}=\frac{24-18\sqrt{2}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18\sqrt{2}}{2*2}=\frac{24+18\sqrt{2}}{4}
$