7p(7-2p)=5(p+4)

Solution for 7p(7-2p)=5(p+4) equation:

7p(7-2p)=5(p+4)

We move all terms to the left:

7p(7-2p)-(5(p+4))=0

We add all the numbers together, and all the variables

7p(-2p+7)-(5(p+4))=0

We multiply parentheses

-14p^2+49p-(5(p+4))=0


We calculate terms in parentheses: -(5(p+4)), so:

5(p+4)

We multiply parentheses

5p+20

Back to the equation:

-(5p+20)


We get rid of parentheses

-14p^2+49p-5p-20=0

We add all the numbers together, and all the variables

-14p^2+44p-20=0

a = -14; b = 44; c = -20;
Δ = b2-4ac
Δ = 442-4·(-14)·(-20)
Δ = 816
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:

$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{51}}{2*-14}=\frac{-44-4\sqrt{51}}{-28}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{51}}{2*-14}=\frac{-44+4\sqrt{51}}{-28}
$