2/3x+18+3x-25=180

Solution for 2/3x+18+3x-25=180 equation:

2/3x+18+3x-25=180

We move all terms to the left:

2/3x+18+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-187=0

We multiply all the terms by the denominator


3x*3x-187*3x+2=0

Wy multiply elements

9x^2-561x+2=0

a = 9; b = -561; c = +2;
Δ = b2-4ac
Δ = -5612-4·9·2
Δ = 314649
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:

$\sqrt{\Delta}=\sqrt{314649}=\sqrt{9*34961}=\sqrt{9}*\sqrt{34961}=3\sqrt{34961}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-561)-3\sqrt{34961}}{2*9}=\frac{561-3\sqrt{34961}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-561)+3\sqrt{34961}}{2*9}=\frac{561+3\sqrt{34961}}{18}
$