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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

3p-(2+2p(p-10))-11=0


We calculate terms in parentheses: -(2+2p(p-10)), so:

2+2p(p-10)

determiningTheFunctionDomain
2p(p-10)+2

We multiply parentheses

2p^2-20p+2

Back to the equation:

-(2p^2-20p+2)


We get rid of parentheses

-2p^2+3p+20p-2-11=0

We add all the numbers together, and all the variables

-2p^2+23p-13=0

a = -2; b = 23; c = -13;
Δ = b2-4ac
Δ = 232-4·(-2)·(-13)
Δ = 425
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:

$\sqrt{\Delta}=\sqrt{425}=\sqrt{25*17}=\sqrt{25}*\sqrt{17}=5\sqrt{17}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-5\sqrt{17}}{2*-2}=\frac{-23-5\sqrt{17}}{-4}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+5\sqrt{17}}{2*-2}=\frac{-23+5\sqrt{17}}{-4}
$