x^2-51x-128=0

Solution for x^2-51x-128=0 equation:

x^2-51x-128=0

a = 1; b = -51; c = -128;
Δ = b2-4ac
Δ = -512-4·1·(-128)
Δ = 3113
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{3113}}{2*1}=\frac{51-\sqrt{3113}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{3113}}{2*1}=\frac{51+\sqrt{3113}}{2}
$