3z^2+4z=2z^2+21

Solution for 3z^2+4z=2z^2+21 equation:

3z^2+4z=2z^2+21

We move all terms to the left:

3z^2+4z-(2z^2+21)=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

z^2+4z-21=0

a = 1; b = 4; c = -21;
Δ = b2-4ac
Δ = 42-4·1·(-21)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-10}{2*1}=\frac{-14}{2}
=-7
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+10}{2*1}=\frac{6}{2}
=3
$