(3x)^2=9(9+16)

Solution for (3x)^2=9(9+16) equation:

(3x)^2=9(9+16)

We move all terms to the left:

(3x)^2-(9(9+16))=0

We add all the numbers together, and all the variables

3x^2-(925)=0

We add all the numbers together, and all the variables

3x^2-925=0

a = 3; b = 0; c = -925;
Δ = b2-4ac
Δ = 02-4·3·(-925)
Δ = 11100
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:

$\sqrt{\Delta}=\sqrt{11100}=\sqrt{100*111}=\sqrt{100}*\sqrt{111}=10\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{111}}{2*3}=\frac{0-10\sqrt{111}}{6}
=-\frac{10\sqrt{111}}{6}
=-\frac{5\sqrt{111}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{111}}{2*3}=\frac{0+10\sqrt{111}}{6}
=\frac{10\sqrt{111}}{6}
=\frac{5\sqrt{111}}{3}
$