(5p-5)(7p+6)=35p-5p-

Solution for (5p-5)(7p+6)=35p-5p- equation:

(5p-5)(7p+6)=35p-5p-

We move all terms to the left:

(5p-5)(7p+6)-(35p-5p-)=0

We add all the numbers together, and all the variables

(5p-5)(7p+6)-(+30p)=0

We get rid of parentheses

(5p-5)(7p+6)-30p=0

We multiply parentheses ..

(+35p^2+30p-35p-30)-30p=0

We get rid of parentheses

35p^2+30p-35p-30p-30=0

We add all the numbers together, and all the variables

35p^2-35p-30=0

a = 35; b = -35; c = -30;
Δ = b2-4ac
Δ = -352-4·35·(-30)
Δ = 5425
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:

$\sqrt{\Delta}=\sqrt{5425}=\sqrt{25*217}=\sqrt{25}*\sqrt{217}=5\sqrt{217}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{217}}{2*35}=\frac{35-5\sqrt{217}}{70}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{217}}{2*35}=\frac{35+5\sqrt{217}}{70}
$