x^2-100x-51=0

Solution for x^2-100x-51=0 equation:

x^2-100x-51=0

a = 1; b = -100; c = -51;
Δ = b2-4ac
Δ = -1002-4·1·(-51)
Δ = 10204
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:

$\sqrt{\Delta}=\sqrt{10204}=\sqrt{4*2551}=\sqrt{4}*\sqrt{2551}=2\sqrt{2551}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2551}}{2*1}=\frac{100-2\sqrt{2551}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2551}}{2*1}=\frac{100+2\sqrt{2551}}{2}
$