5(2p-4)(p+45)=25

Solution for 5(2p-4)(p+45)=25 equation:

5(2p-4)(p+45)=25

We move all terms to the left:

5(2p-4)(p+45)-(25)=0

We multiply parentheses ..

5(+2p^2+90p-4p-180)-25=0

We multiply parentheses

10p^2+450p-20p-900-25=0

We add all the numbers together, and all the variables

10p^2+430p-925=0

a = 10; b = 430; c = -925;
Δ = b2-4ac
Δ = 4302-4·10·(-925)
Δ = 221900
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:

$\sqrt{\Delta}=\sqrt{221900}=\sqrt{100*2219}=\sqrt{100}*\sqrt{2219}=10\sqrt{2219}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(430)-10\sqrt{2219}}{2*10}=\frac{-430-10\sqrt{2219}}{20}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(430)+10\sqrt{2219}}{2*10}=\frac{-430+10\sqrt{2219}}{20}
$