16x^2-2x-144=0

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

16x^2-2x-144=0

a = 16; b = -2; c = -144;
Δ = b2-4ac
Δ = -22-4·16·(-144)
Δ = 9220
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:

$\sqrt{\Delta}=\sqrt{9220}=\sqrt{4*2305}=\sqrt{4}*\sqrt{2305}=2\sqrt{2305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{2305}}{2*16}=\frac{2-2\sqrt{2305}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{2305}}{2*16}=\frac{2+2\sqrt{2305}}{32}
$