90=z2+46

Solution for 90=z2+46 equation:

90=z2+46

We move all terms to the left:

90-(z2+46)=0

We add all the numbers together, and all the variables

-(+z^2+46)+90=0

We get rid of parentheses

-z^2-46+90=0

We add all the numbers together, and all the variables

-1z^2+44=0

a = -1; b = 0; c = +44;
Δ = b2-4ac
Δ = 02-4·(-1)·44
Δ = 176
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{11}}{2*-1}=\frac{0-4\sqrt{11}}{-2}
=-\frac{4\sqrt{11}}{-2}
=-\frac{2\sqrt{11}}{-1}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{11}}{2*-1}=\frac{0+4\sqrt{11}}{-2}
=\frac{4\sqrt{11}}{-2}
=\frac{2\sqrt{11}}{-1}
$