29(3x+-2)+12/3x=30

Solution for 29(3x+-2)+12/3x=30 equation:

29(3x+-2)+12/3x=30

We move all terms to the left:

29(3x+-2)+12/3x-(30)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

29(3x-2)+12/3x-30=0

We multiply parentheses

87x+12/3x-58-30=0

We multiply all the terms by the denominator


87x*3x-58*3x-30*3x+12=0

Wy multiply elements

261x^2-174x-90x+12=0

We add all the numbers together, and all the variables

261x^2-264x+12=0

a = 261; b = -264; c = +12;
Δ = b2-4ac
Δ = -2642-4·261·12
Δ = 57168
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:

$\sqrt{\Delta}=\sqrt{57168}=\sqrt{144*397}=\sqrt{144}*\sqrt{397}=12\sqrt{397}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-12\sqrt{397}}{2*261}=\frac{264-12\sqrt{397}}{522}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+12\sqrt{397}}{2*261}=\frac{264+12\sqrt{397}}{522}
$