(3x)^2+5^2=214

Solution for (3x)^2+5^2=214 equation:

(3x)^2+5^2=214

We move all terms to the left:

(3x)^2+5^2-(214)=0

determiningTheFunctionDomain
3x^2-214+5^2=0

We add all the numbers together, and all the variables

3x^2-189=0

a = 3; b = 0; c = -189;
Δ = b2-4ac
Δ = 02-4·3·(-189)
Δ = 2268
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:

$\sqrt{\Delta}=\sqrt{2268}=\sqrt{324*7}=\sqrt{324}*\sqrt{7}=18\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{7}}{2*3}=\frac{0-18\sqrt{7}}{6}
=-\frac{18\sqrt{7}}{6}
=-3\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{7}}{2*3}=\frac{0+18\sqrt{7}}{6}
=\frac{18\sqrt{7}}{6}
=3\sqrt{7}
$