-11+10p(p+10)=2(2p+11)+4

Solution for -11+10p(p+10)=2(2p+11)+4 equation:

-11+10p(p+10)=2(2p+11)+4

We move all terms to the left:

-11+10p(p+10)-(2(2p+11)+4)=0

We multiply parentheses

10p^2+100p-(2(2p+11)+4)-11=0


We calculate terms in parentheses: -(2(2p+11)+4), so:

2(2p+11)+4

We multiply parentheses

4p+22+4

We add all the numbers together, and all the variables

4p+26

Back to the equation:

-(4p+26)


We get rid of parentheses

10p^2+100p-4p-26-11=0

We add all the numbers together, and all the variables

10p^2+96p-37=0

a = 10; b = 96; c = -37;
Δ = b2-4ac
Δ = 962-4·10·(-37)
Δ = 10696
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:

$\sqrt{\Delta}=\sqrt{10696}=\sqrt{4*2674}=\sqrt{4}*\sqrt{2674}=2\sqrt{2674}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-2\sqrt{2674}}{2*10}=\frac{-96-2\sqrt{2674}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+2\sqrt{2674}}{2*10}=\frac{-96+2\sqrt{2674}}{20}
$