4x^2-16x-65=8

Solution for 4x^2-16x-65=8 equation:

4x^2-16x-65=8

We move all terms to the left:

4x^2-16x-65-(8)=0

We add all the numbers together, and all the variables

4x^2-16x-73=0

a = 4; b = -16; c = -73;
Δ = b2-4ac
Δ = -162-4·4·(-73)
Δ = 1424
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:

$\sqrt{\Delta}=\sqrt{1424}=\sqrt{16*89}=\sqrt{16}*\sqrt{89}=4\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{89}}{2*4}=\frac{16-4\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{89}}{2*4}=\frac{16+4\sqrt{89}}{8}
$