z^2+9z=10

Solution for z^2+9z=10 equation:

z^2+9z=10

We move all terms to the left:

z^2+9z-(10)=0

a = 1; b = 9; c = -10;
Δ = b2-4ac
Δ = 92-4·1·(-10)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-11}{2*1}=\frac{-20}{2}
=-10
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+11}{2*1}=\frac{2}{2}
=1
$