3x-6=9/2x+15=8

Solution for 3x-6=9/2x+15=8 equation:

3x-6=9/2x+15=8

We move all terms to the left:

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


Domain of the equation: 2x+15)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

6x^2-42x-9=0

a = 6; b = -42; c = -9;
Δ = b2-4ac
Δ = -422-4·6·(-9)
Δ = 1980
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:

$\sqrt{\Delta}=\sqrt{1980}=\sqrt{36*55}=\sqrt{36}*\sqrt{55}=6\sqrt{55}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{55}}{2*6}=\frac{42-6\sqrt{55}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{55}}{2*6}=\frac{42+6\sqrt{55}}{12}
$