(x*3)(x*5)=9

Solution for (x*3)(x*5)=9 equation:

(x*3)(x*5)=9

We move all terms to the left:

(x*3)(x*5)-(9)=0

We add all the numbers together, and all the variables

(+x*3)(+x*5)-9=0

We multiply parentheses ..

(+15x^2)-9=0

We get rid of parentheses

15x^2-9=0

a = 15; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·15·(-9)
Δ = 540
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:

$\sqrt{\Delta}=\sqrt{540}=\sqrt{36*15}=\sqrt{36}*\sqrt{15}=6\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{15}}{2*15}=\frac{0-6\sqrt{15}}{30}
=-\frac{6\sqrt{15}}{30}
=-\frac{\sqrt{15}}{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{15}}{2*15}=\frac{0+6\sqrt{15}}{30}
=\frac{6\sqrt{15}}{30}
=\frac{\sqrt{15}}{5}
$