-3z(z+7)=4z

Solution for -3z(z+7)=4z equation:

-3z(z+7)=4z

We move all terms to the left:

-3z(z+7)-(4z)=0

We add all the numbers together, and all the variables

-4z-3z(z+7)=0

We multiply parentheses

-3z^2-4z-21z=0

We add all the numbers together, and all the variables

-3z^2-25z=0

a = -3; b = -25; c = 0;
Δ = b2-4ac
Δ = -252-4·(-3)·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-25}{2*-3}=\frac{0}{-6}
=0
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+25}{2*-3}=\frac{50}{-6}
=-8+1/3
$