x^2+21x-126=0

Solution for x^2+21x-126=0 equation:

x^2+21x-126=0

a = 1; b = 21; c = -126;
Δ = b2-4ac
Δ = 212-4·1·(-126)
Δ = 945
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:

$\sqrt{\Delta}=\sqrt{945}=\sqrt{9*105}=\sqrt{9}*\sqrt{105}=3\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{105}}{2*1}=\frac{-21-3\sqrt{105}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{105}}{2*1}=\frac{-21+3\sqrt{105}}{2}
$