4X^2-16x-54-1-4=0

Solution for 4X^2-16x-54-1-4=0 equation:

4X^2-16X-54-1-4=0

We add all the numbers together, and all the variables

4X^2-16X-59=0

a = 4; b = -16; c = -59;
Δ = b2-4ac
Δ = -162-4·4·(-59)
Δ = 1200
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:

$\sqrt{\Delta}=\sqrt{1200}=\sqrt{400*3}=\sqrt{400}*\sqrt{3}=20\sqrt{3}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-20\sqrt{3}}{2*4}=\frac{16-20\sqrt{3}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+20\sqrt{3}}{2*4}=\frac{16+20\sqrt{3}}{8}
$