-p(p-3)=3p-7

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Solution for -p(p-3)=3p-7 equation:



-p(p-3)=3p-7
We move all terms to the left:
-p(p-3)-(3p-7)=0
We multiply parentheses
-p^2+3p-(3p-7)=0
We get rid of parentheses
-p^2+3p-3p+7=0
We add all the numbers together, and all the variables
-1p^2+7=0
a = -1; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-1)·7
Δ = 28
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:
$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$p_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*-1}=\frac{0-2\sqrt{7}}{-2} =-\frac{2\sqrt{7}}{-2} =-\frac{\sqrt{7}}{-1} $
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*-1}=\frac{0+2\sqrt{7}}{-2} =\frac{2\sqrt{7}}{-2} =\frac{\sqrt{7}}{-1} $

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