5p-17=2p(2p-7)

Solution for 5p-17=2p(2p-7) equation:

5p-17=2p(2p-7)

We move all terms to the left:

5p-17-(2p(2p-7))=0


We calculate terms in parentheses: -(2p(2p-7)), so:

2p(2p-7)

We multiply parentheses

4p^2-14p

Back to the equation:

-(4p^2-14p)


We get rid of parentheses

-4p^2+5p+14p-17=0

We add all the numbers together, and all the variables

-4p^2+19p-17=0

a = -4; b = 19; c = -17;
Δ = b2-4ac
Δ = 192-4·(-4)·(-17)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-\sqrt{89}}{2*-4}=\frac{-19-\sqrt{89}}{-8}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{89}}{2*-4}=\frac{-19+\sqrt{89}}{-8}
$