3z^2-5z=2z^2+14=

Solution for 3z^2-5z=2z^2+14= equation:

3z^2-5z=2z^2+14=

We move all terms to the left:

3z^2-5z-(2z^2+14)=0

We get rid of parentheses

3z^2-2z^2-5z-14=0

We add all the numbers together, and all the variables

z^2-5z-14=0

a = 1; b = -5; c = -14;
Δ = b2-4ac
Δ = -52-4·1·(-14)
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*1}=\frac{-4}{2}
=-2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*1}=\frac{14}{2}
=7
$