X2-28x+127=0

Solution for X2-28x+127=0 equation:

X2-28X+127=0

We add all the numbers together, and all the variables

X^2-28X+127=0

a = 1; b = -28; c = +127;
Δ = b2-4ac
Δ = -282-4·1·127
Δ = 276
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:

$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{69}}{2*1}=\frac{28-2\sqrt{69}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{69}}{2*1}=\frac{28+2\sqrt{69}}{2}
$