3x=225/5x

Solution for 3x=225/5x equation:

3x=225/5x

We move all terms to the left:

3x-(225/5x)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(+225/5x)=0

We get rid of parentheses

3x-225/5x=0

We multiply all the terms by the denominator


3x*5x-225=0

Wy multiply elements

15x^2-225=0

a = 15; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·15·(-225)
Δ = 13500
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:

$\sqrt{\Delta}=\sqrt{13500}=\sqrt{900*15}=\sqrt{900}*\sqrt{15}=30\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{15}}{2*15}=\frac{0-30\sqrt{15}}{30}
=-\frac{30\sqrt{15}}{30}
=-\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{15}}{2*15}=\frac{0+30\sqrt{15}}{30}
=\frac{30\sqrt{15}}{30}
=\sqrt{15}
$