4x^2-24x-89=0

Solution for 4x^2-24x-89=0 equation:

4x^2-24x-89=0

a = 4; b = -24; c = -89;
Δ = b2-4ac
Δ = -242-4·4·(-89)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-20\sqrt{5}}{2*4}=\frac{24-20\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+20\sqrt{5}}{2*4}=\frac{24+20\sqrt{5}}{8}
$