P=(2a-1)(4a-7)

Solution for P=(2a-1)(4a-7) equation:

=(2P-1)(4P-7)

We move all terms to the left:

-((2P-1)(4P-7))=0

We multiply parentheses ..

-((+8P^2-14P-4P+7))=0


We calculate terms in parentheses: -((+8P^2-14P-4P+7)), so:

(+8P^2-14P-4P+7)

We get rid of parentheses

8P^2-14P-4P+7

We add all the numbers together, and all the variables

8P^2-18P+7

Back to the equation:

-(8P^2-18P+7)


We get rid of parentheses

-8P^2+18P-7=0

a = -8; b = 18; c = -7;
Δ = b2-4ac
Δ = 182-4·(-8)·(-7)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$P_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-10}{2*-8}=\frac{-28}{-16}
=1+3/4
$
$P_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+10}{2*-8}=\frac{-8}{-16}
=1/2
$