9(7+4x^2)+16x^2=323

Solution for 9(7+4x^2)+16x^2=323 equation:

9(7+4x^2)+16x^2=323

We move all terms to the left:

9(7+4x^2)+16x^2-(323)=0

We add all the numbers together, and all the variables

16x^2+9(7+4x^2)-323=0

We multiply parentheses

16x^2+36x^2+63-323=0

We add all the numbers together, and all the variables

52x^2-260=0

a = 52; b = 0; c = -260;
Δ = b2-4ac
Δ = 02-4·52·(-260)
Δ = 54080
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:

$\sqrt{\Delta}=\sqrt{54080}=\sqrt{10816*5}=\sqrt{10816}*\sqrt{5}=104\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-104\sqrt{5}}{2*52}=\frac{0-104\sqrt{5}}{104}
=-\frac{104\sqrt{5}}{104}
=-\sqrt{5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+104\sqrt{5}}{2*52}=\frac{0+104\sqrt{5}}{104}
=\frac{104\sqrt{5}}{104}
=\sqrt{5}
$