Y=p^2+7p=6

Solution for Y=p^2+7p=6 equation:

=Y^2+7Y=6

We move all terms to the left:

-(Y^2+7Y)=0

We get rid of parentheses

-Y^2-7Y=0

We add all the numbers together, and all the variables

-1Y^2-7Y=0

a = -1; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·(-1)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*-1}=\frac{0}{-2}
=0
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*-1}=\frac{14}{-2}
=-7
$