3x-25=2/3x+18

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

3x-25=2/3x+18

We move all terms to the left:

3x-25-(2/3x+18)=0


Domain of the equation: 3x+18)!=0

x∈R


We get rid of parentheses

3x-2/3x-18-25=0

We multiply all the terms by the denominator


3x*3x-18*3x-25*3x-2=0

Wy multiply elements

9x^2-54x-75x-2=0

We add all the numbers together, and all the variables

9x^2-129x-2=0

a = 9; b = -129; c = -2;
Δ = b2-4ac
Δ = -1292-4·9·(-2)
Δ = 16713
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:

$\sqrt{\Delta}=\sqrt{16713}=\sqrt{9*1857}=\sqrt{9}*\sqrt{1857}=3\sqrt{1857}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-129)-3\sqrt{1857}}{2*9}=\frac{129-3\sqrt{1857}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-129)+3\sqrt{1857}}{2*9}=\frac{129+3\sqrt{1857}}{18}
$