(8p+6)(9p-1)=180

Solution for (8p+6)(9p-1)=180 equation:

(8p+6)(9p-1)=180

We move all terms to the left:

(8p+6)(9p-1)-(180)=0

We multiply parentheses ..

(+72p^2-8p+54p-6)-180=0

We get rid of parentheses

72p^2-8p+54p-6-180=0

We add all the numbers together, and all the variables

72p^2+46p-186=0

a = 72; b = 46; c = -186;
Δ = b2-4ac
Δ = 462-4·72·(-186)
Δ = 55684
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:

$\sqrt{\Delta}=\sqrt{55684}=\sqrt{4*13921}=\sqrt{4}*\sqrt{13921}=2\sqrt{13921}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-2\sqrt{13921}}{2*72}=\frac{-46-2\sqrt{13921}}{144}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+2\sqrt{13921}}{2*72}=\frac{-46+2\sqrt{13921}}{144}
$