z(z+7)=30

Solution for z(z+7)=30 equation:

z(z+7)=30

We move all terms to the left:

z(z+7)-(30)=0

We multiply parentheses

z^2+7z-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:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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