4+9x2=72

Solution for 4+9x2=72 equation:

4+9x^2=72

We move all terms to the left:

4+9x^2-(72)=0

We add all the numbers together, and all the variables

9x^2-68=0

a = 9; b = 0; c = -68;
Δ = b2-4ac
Δ = 02-4·9·(-68)
Δ = 2448
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:

$\sqrt{\Delta}=\sqrt{2448}=\sqrt{144*17}=\sqrt{144}*\sqrt{17}=12\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{17}}{2*9}=\frac{0-12\sqrt{17}}{18}
=-\frac{12\sqrt{17}}{18}
=-\frac{2\sqrt{17}}{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{17}}{2*9}=\frac{0+12\sqrt{17}}{18}
=\frac{12\sqrt{17}}{18}
=\frac{2\sqrt{17}}{3}
$