4x^2-9x-54=0

Solution for 4x^2-9x-54=0 equation:

4x^2-9x-54=0

a = 4; b = -9; c = -54;
Δ = b2-4ac
Δ = -92-4·4·(-54)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{105}}{2*4}=\frac{9-3\sqrt{105}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{105}}{2*4}=\frac{9+3\sqrt{105}}{8}
$