b^2-24b-21=0

Solution for b^2-24b-21=0 equation:

b^2-24b-21=0

a = 1; b = -24; c = -21;
Δ = b2-4ac
Δ = -242-4·1·(-21)
Δ = 660
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-2\sqrt{165}}{2*1}=\frac{24-2\sqrt{165}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+2\sqrt{165}}{2*1}=\frac{24+2\sqrt{165}}{2}
$