2z^2-5z-12=z^2-15

Solution for 2z^2-5z-12=z^2-15 equation:

2z^2-5z-12=z^2-15

We move all terms to the left:

2z^2-5z-12-(z^2-15)=0

We get rid of parentheses

2z^2-z^2-5z+15-12=0

We add all the numbers together, and all the variables

z^2-5z+3=0

a = 1; b = -5; c = +3;
Δ = b2-4ac
Δ = -52-4·1·3
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{13}}{2*1}=\frac{5-\sqrt{13}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{13}}{2*1}=\frac{5+\sqrt{13}}{2}
$