X^2-42x+21=0

Solution for X^2-42x+21=0 equation:

X^2-42X+21=0

a = 1; b = -42; c = +21;
Δ = b2-4ac
Δ = -422-4·1·21
Δ = 1680
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:

$\sqrt{\Delta}=\sqrt{1680}=\sqrt{16*105}=\sqrt{16}*\sqrt{105}=4\sqrt{105}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-4\sqrt{105}}{2*1}=\frac{42-4\sqrt{105}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+4\sqrt{105}}{2*1}=\frac{42+4\sqrt{105}}{2}
$