4z(z=7)

Solution for 4z(z=7) equation:

4z(z=7)

We move all terms to the left:

4z(z-(7))=0

We multiply parentheses

4z^2-28z=0

a = 4; b = -28; c = 0;
Δ = b2-4ac
Δ = -282-4·4·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-28}{2*4}=\frac{0}{8}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+28}{2*4}=\frac{56}{8}
=7
$