x2-21x-252=0

Solution for x2-21x-252=0 equation:

x2-21x-252=0

We add all the numbers together, and all the variables

x^2-21x-252=0

a = 1; b = -21; c = -252;
Δ = b2-4ac
Δ = -212-4·1·(-252)
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{161}}{2*1}=\frac{21-3\sqrt{161}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{161}}{2*1}=\frac{21+3\sqrt{161}}{2}
$