6p-5(7p+5)=-p(p+21)

Solution for 6p-5(7p+5)=-p(p+21) equation:

6p-5(7p+5)=-p(p+21)

We move all terms to the left:

6p-5(7p+5)-(-p(p+21))=0

We multiply parentheses

6p-35p-(-p(p+21))-25=0


We calculate terms in parentheses: -(-p(p+21)), so:

-p(p+21)

We multiply parentheses

-p^2-21p

We add all the numbers together, and all the variables

-1p^2-21p

Back to the equation:

-(-1p^2-21p)


We add all the numbers together, and all the variables

-(-1p^2-21p)-29p-25=0

We get rid of parentheses

1p^2+21p-29p-25=0

We add all the numbers together, and all the variables

p^2-8p-25=0

a = 1; b = -8; c = -25;
Δ = b2-4ac
Δ = -82-4·1·(-25)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{41}}{2*1}=\frac{8-2\sqrt{41}}{2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{41}}{2*1}=\frac{8+2\sqrt{41}}{2}
$