(5p+2)(7p+4)=90

Solution for (5p+2)(7p+4)=90 equation:

(5p+2)(7p+4)=90

We move all terms to the left:

(5p+2)(7p+4)-(90)=0

We multiply parentheses ..

(+35p^2+20p+14p+8)-90=0

We get rid of parentheses

35p^2+20p+14p+8-90=0

We add all the numbers together, and all the variables

35p^2+34p-82=0

a = 35; b = 34; c = -82;
Δ = b2-4ac
Δ = 342-4·35·(-82)
Δ = 12636
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:

$\sqrt{\Delta}=\sqrt{12636}=\sqrt{324*39}=\sqrt{324}*\sqrt{39}=18\sqrt{39}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-18\sqrt{39}}{2*35}=\frac{-34-18\sqrt{39}}{70}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+18\sqrt{39}}{2*35}=\frac{-34+18\sqrt{39}}{70}
$