z2+11z+9=52

Solution for z2+11z+9=52 equation:

z2+11z+9=52

We move all terms to the left:

z2+11z+9-(52)=0

We add all the numbers together, and all the variables

z^2+11z-43=0

a = 1; b = 11; c = -43;
Δ = b2-4ac
Δ = 112-4·1·(-43)
Δ = 293
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{-(11)-\sqrt{293}}{2*1}=\frac{-11-\sqrt{293}}{2}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{293}}{2*1}=\frac{-11+\sqrt{293}}{2}
$