8p(p-0.25)=4(2p-0.5)

Solution for 8p(p-0.25)=4(2p-0.5) equation:

8p(p-0.25)=4(2p-0.5)

We move all terms to the left:

8p(p-0.25)-(4(2p-0.5))=0

We multiply parentheses

8p^2-2p-(4(2p-0.5))=0


We calculate terms in parentheses: -(4(2p-0.5)), so:

4(2p-0.5)

We multiply parentheses

8p-2

Back to the equation:

-(8p-2)


We get rid of parentheses

8p^2-2p-8p+2=0

We add all the numbers together, and all the variables

8p^2-10p+2=0

a = 8; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·8·2
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6}{2*8}=\frac{4}{16}
=1/4
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6}{2*8}=\frac{16}{16}
=1
$