p^2+10p-59=9

Solution for p^2+10p-59=9 equation:

p^2+10p-59=9

We move all terms to the left:

p^2+10p-59-(9)=0

We add all the numbers together, and all the variables

p^2+10p-68=0

a = 1; b = 10; c = -68;
Δ = b2-4ac
Δ = 102-4·1·(-68)
Δ = 372
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{93}}{2*1}=\frac{-10-2\sqrt{93}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{93}}{2*1}=\frac{-10+2\sqrt{93}}{2}
$