b^2-12b-76=0

Solution for b^2-12b-76=0 equation:

b^2-12b-76=0

a = 1; b = -12; c = -76;
Δ = b2-4ac
Δ = -122-4·1·(-76)
Δ = 448
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:

$\sqrt{\Delta}=\sqrt{448}=\sqrt{64*7}=\sqrt{64}*\sqrt{7}=8\sqrt{7}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-8\sqrt{7}}{2*1}=\frac{12-8\sqrt{7}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+8\sqrt{7}}{2*1}=\frac{12+8\sqrt{7}}{2}
$