12x^2+9^2=144

Solution for 12x^2+9^2=144 equation:

12x^2+9^2=144

We move all terms to the left:

12x^2+9^2-(144)=0

determiningTheFunctionDomain
12x^2-144+9^2=0

We add all the numbers together, and all the variables

12x^2-63=0

a = 12; b = 0; c = -63;
Δ = b2-4ac
Δ = 02-4·12·(-63)
Δ = 3024
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:

$\sqrt{\Delta}=\sqrt{3024}=\sqrt{144*21}=\sqrt{144}*\sqrt{21}=12\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{21}}{2*12}=\frac{0-12\sqrt{21}}{24}
=-\frac{12\sqrt{21}}{24}
=-\frac{\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{21}}{2*12}=\frac{0+12\sqrt{21}}{24}
=\frac{12\sqrt{21}}{24}
=\frac{\sqrt{21}}{2}
$