r^2-12r-42=0

Solution for r^2-12r-42=0 equation:

r^2-12r-42=0

a = 1; b = -12; c = -42;
Δ = b2-4ac
Δ = -122-4·1·(-42)
Δ = 312
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{312}=\sqrt{4*78}=\sqrt{4}*\sqrt{78}=2\sqrt{78}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{78}}{2*1}=\frac{12-2\sqrt{78}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{78}}{2*1}=\frac{12+2\sqrt{78}}{2}
$