Y=b^2+7b-30

Solution for Y=b^2+7b-30 equation:

=Y^2+7Y-30

We move all terms to the left:

-(Y^2+7Y-30)=0

We get rid of parentheses

-Y^2-7Y+30=0

We add all the numbers together, and all the variables

-1Y^2-7Y+30=0

a = -1; b = -7; c = +30;
Δ = b2-4ac
Δ = -72-4·(-1)·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$Y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-1}=\frac{-6}{-2}
=+3
$
$Y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-1}=\frac{20}{-2}
=-10
$