16x^2-144-2268=0

Solution for 16x^2-144-2268=0 equation:

16x^2-144-2268=0

We add all the numbers together, and all the variables

16x^2-2412=0

a = 16; b = 0; c = -2412;
Δ = b2-4ac
Δ = 02-4·16·(-2412)
Δ = 154368
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:

$\sqrt{\Delta}=\sqrt{154368}=\sqrt{2304*67}=\sqrt{2304}*\sqrt{67}=48\sqrt{67}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{67}}{2*16}=\frac{0-48\sqrt{67}}{32}
=-\frac{48\sqrt{67}}{32}
=-\frac{3\sqrt{67}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{67}}{2*16}=\frac{0+48\sqrt{67}}{32}
=\frac{48\sqrt{67}}{32}
=\frac{3\sqrt{67}}{2}
$