2p^2=-10p-11

Solution for 2p^2=-10p-11 equation:

2p^2=-10p-11

We move all terms to the left:

2p^2-(-10p-11)=0

We get rid of parentheses

2p^2+10p+11=0

a = 2; b = 10; c = +11;
Δ = b2-4ac
Δ = 102-4·2·11
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{3}}{2*2}=\frac{-10-2\sqrt{3}}{4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{3}}{2*2}=\frac{-10+2\sqrt{3}}{4}
$