3x-9/2x=15

Solution for 3x-9/2x=15 equation:

3x-9/2x=15

We move all terms to the left:

3x-9/2x-(15)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


3x*2x-15*2x-9=0

Wy multiply elements

6x^2-30x-9=0

a = 6; b = -30; c = -9;
Δ = b2-4ac
Δ = -302-4·6·(-9)
Δ = 1116
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:

$\sqrt{\Delta}=\sqrt{1116}=\sqrt{36*31}=\sqrt{36}*\sqrt{31}=6\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{31}}{2*6}=\frac{30-6\sqrt{31}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{31}}{2*6}=\frac{30+6\sqrt{31}}{12}
$