4x^2-24x-54=0

Solution for 4x^2-24x-54=0 equation:

4x^2-24x-54=0

a = 4; b = -24; c = -54;
Δ = b2-4ac
Δ = -242-4·4·(-54)
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{10}}{2*4}=\frac{24-12\sqrt{10}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{10}}{2*4}=\frac{24+12\sqrt{10}}{8}
$