3(x+5)=30/5x

Solution for 3(x+5)=30/5x equation:

3(x+5)=30/5x

We move all terms to the left:

3(x+5)-(30/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3(x+5)-(+30/5x)=0

We multiply parentheses

3x-(+30/5x)+15=0

We get rid of parentheses

3x-30/5x+15=0

We multiply all the terms by the denominator


3x*5x+15*5x-30=0

Wy multiply elements

15x^2+75x-30=0

a = 15; b = 75; c = -30;
Δ = b2-4ac
Δ = 752-4·15·(-30)
Δ = 7425
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:

$\sqrt{\Delta}=\sqrt{7425}=\sqrt{225*33}=\sqrt{225}*\sqrt{33}=15\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(75)-15\sqrt{33}}{2*15}=\frac{-75-15\sqrt{33}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(75)+15\sqrt{33}}{2*15}=\frac{-75+15\sqrt{33}}{30}
$