3x-15=9/2x-6

Solution for 3x-15=9/2x-6 equation:

3x-15=9/2x-6

We move all terms to the left:

3x-15-(9/2x-6)=0


Domain of the equation: 2x-6)!=0

x∈R


We get rid of parentheses

3x-9/2x+6-15=0

We multiply all the terms by the denominator


3x*2x+6*2x-15*2x-9=0

Wy multiply elements

6x^2+12x-30x-9=0

We add all the numbers together, and all the variables

6x^2-18x-9=0

a = 6; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·6·(-9)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{15}}{2*6}=\frac{18-6\sqrt{15}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{15}}{2*6}=\frac{18+6\sqrt{15}}{12}
$