4x^2-24x-5=0

Solution for 4x^2-24x-5=0 equation:

4x^2-24x-5=0

a = 4; b = -24; c = -5;
Δ = b2-4ac
Δ = -242-4·4·(-5)
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-4\sqrt{41}}{2*4}=\frac{24-4\sqrt{41}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+4\sqrt{41}}{2*4}=\frac{24+4\sqrt{41}}{8}
$