5x^2-8x-144=0

Solution for 5x^2-8x-144=0 equation:

5x^2-8x-144=0

a = 5; b = -8; c = -144;
Δ = b2-4ac
Δ = -82-4·5·(-144)
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8\sqrt{46}}{2*5}=\frac{8-8\sqrt{46}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8\sqrt{46}}{2*5}=\frac{8+8\sqrt{46}}{10}
$