6x+3/2x=9

Solution for 6x+3/2x=9 equation:

6x+3/2x=9

We move all terms to the left:

6x+3/2x-(9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


6x*2x-9*2x+3=0

Wy multiply elements

12x^2-18x+3=0

a = 12; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·12·3
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{5}}{2*12}=\frac{18-6\sqrt{5}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{5}}{2*12}=\frac{18+6\sqrt{5}}{24}
$