3(x+5)=2/3x-15

Solution for 3(x+5)=2/3x-15 equation:

3(x+5)=2/3x-15

We move all terms to the left:

3(x+5)-(2/3x-15)=0


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

x∈R


We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

9x^2+90x-2=0

a = 9; b = 90; c = -2;
Δ = b2-4ac
Δ = 902-4·9·(-2)
Δ = 8172
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:

$\sqrt{\Delta}=\sqrt{8172}=\sqrt{36*227}=\sqrt{36}*\sqrt{227}=6\sqrt{227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{227}}{2*9}=\frac{-90-6\sqrt{227}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{227}}{2*9}=\frac{-90+6\sqrt{227}}{18}
$