8x^2-3x-144=0

Solution for 8x^2-3x-144=0 equation:

8x^2-3x-144=0

a = 8; b = -3; c = -144;
Δ = b2-4ac
Δ = -32-4·8·(-144)
Δ = 4617
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:

$\sqrt{\Delta}=\sqrt{4617}=\sqrt{81*57}=\sqrt{81}*\sqrt{57}=9\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-9\sqrt{57}}{2*8}=\frac{3-9\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+9\sqrt{57}}{2*8}=\frac{3+9\sqrt{57}}{16}
$