9(3x-2)=5/2x+3

Solution for 9(3x-2)=5/2x+3 equation:

9(3x-2)=5/2x+3

We move all terms to the left:

9(3x-2)-(5/2x+3)=0


Domain of the equation: 2x+3)!=0

x∈R


We multiply parentheses

27x-(5/2x+3)-18=0

We get rid of parentheses

27x-5/2x-3-18=0

We multiply all the terms by the denominator


27x*2x-3*2x-18*2x-5=0

Wy multiply elements

54x^2-6x-36x-5=0

We add all the numbers together, and all the variables

54x^2-42x-5=0

a = 54; b = -42; c = -5;
Δ = b2-4ac
Δ = -422-4·54·(-5)
Δ = 2844
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:

$\sqrt{\Delta}=\sqrt{2844}=\sqrt{36*79}=\sqrt{36}*\sqrt{79}=6\sqrt{79}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{79}}{2*54}=\frac{42-6\sqrt{79}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{79}}{2*54}=\frac{42+6\sqrt{79}}{108}
$