10-(p+3)p=7

Solution for 10-(p+3)p=7 equation:

10-(p+3)p=7

We move all terms to the left:

10-(p+3)p-(7)=0

We add all the numbers together, and all the variables

-(p+3)p+3=0

We multiply parentheses

-p^2-3p+3=0

We add all the numbers together, and all the variables

-1p^2-3p+3=0

a = -1; b = -3; c = +3;
Δ = b2-4ac
Δ = -32-4·(-1)·3
Δ = 21
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{-(-3)-\sqrt{21}}{2*-1}=\frac{3-\sqrt{21}}{-2}
$
$p_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{21}}{2*-1}=\frac{3+\sqrt{21}}{-2}
$