9x-3/2x=12

Solution for 9x-3/2x=12 equation:

9x-3/2x=12

We move all terms to the left:

9x-3/2x-(12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


9x*2x-12*2x-3=0

Wy multiply elements

18x^2-24x-3=0

a = 18; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·18·(-3)
Δ = 792
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:

$\sqrt{\Delta}=\sqrt{792}=\sqrt{36*22}=\sqrt{36}*\sqrt{22}=6\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{22}}{2*18}=\frac{24-6\sqrt{22}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{22}}{2*18}=\frac{24+6\sqrt{22}}{36}
$