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

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

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

We move all terms to the left:

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


Domain of the equation: 5x-15)!=0

x∈R


We multiply parentheses

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

We get rid of parentheses

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

We multiply all the terms by the denominator


3x*5x+15*5x+15*5x-2=0

Wy multiply elements

15x^2+75x+75x-2=0

We add all the numbers together, and all the variables

15x^2+150x-2=0

a = 15; b = 150; c = -2;
Δ = b2-4ac
Δ = 1502-4·15·(-2)
Δ = 22620
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:

$\sqrt{\Delta}=\sqrt{22620}=\sqrt{4*5655}=\sqrt{4}*\sqrt{5655}=2\sqrt{5655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{5655}}{2*15}=\frac{-150-2\sqrt{5655}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{5655}}{2*15}=\frac{-150+2\sqrt{5655}}{30}
$