(z+18)(z-18)=z+49

Solution for (z+18)(z-18)=z+49 equation:

(z+18)(z-18)=z+49

We move all terms to the left:

(z+18)(z-18)-(z+49)=0

We use the square of the difference formula

z^2-(z+49)-324=0

We get rid of parentheses

z^2-z-49-324=0

We add all the numbers together, and all the variables

z^2-1z-373=0

a = 1; b = -1; c = -373;
Δ = b2-4ac
Δ = -12-4·1·(-373)
Δ = 1493
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{-(-1)-\sqrt{1493}}{2*1}=\frac{1-\sqrt{1493}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1493}}{2*1}=\frac{1+\sqrt{1493}}{2}
$