2/3x+27+3x-25=180

Solution for 2/3x+27+3x-25=180 equation:

2/3x+27+3x-25=180

We move all terms to the left:

2/3x+27+3x-25-(180)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

3x+2/3x-178=0

We multiply all the terms by the denominator


3x*3x-178*3x+2=0

Wy multiply elements

9x^2-534x+2=0

a = 9; b = -534; c = +2;
Δ = b2-4ac
Δ = -5342-4·9·2
Δ = 285084
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:

$\sqrt{\Delta}=\sqrt{285084}=\sqrt{36*7919}=\sqrt{36}*\sqrt{7919}=6\sqrt{7919}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-534)-6\sqrt{7919}}{2*9}=\frac{534-6\sqrt{7919}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-534)+6\sqrt{7919}}{2*9}=\frac{534+6\sqrt{7919}}{18}
$