3(x+15)=2/3x-15

Solution for 3(x+15)=2/3x-15 equation:

3(x+15)=2/3x-15

We move all terms to the left:

3(x+15)-(2/3x-15)=0


Domain of the equation: 3x-15)!=0

x∈R


We multiply parentheses

3x-(2/3x-15)+45=0

We get rid of parentheses

3x-2/3x+15+45=0

We multiply all the terms by the denominator


3x*3x+15*3x+45*3x-2=0

Wy multiply elements

9x^2+45x+135x-2=0

We add all the numbers together, and all the variables

9x^2+180x-2=0

a = 9; b = 180; c = -2;
Δ = b2-4ac
Δ = 1802-4·9·(-2)
Δ = 32472
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:

$\sqrt{\Delta}=\sqrt{32472}=\sqrt{36*902}=\sqrt{36}*\sqrt{902}=6\sqrt{902}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(180)-6\sqrt{902}}{2*9}=\frac{-180-6\sqrt{902}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(180)+6\sqrt{902}}{2*9}=\frac{-180+6\sqrt{902}}{18}
$