5z^2-9=46

Solution for 5z^2-9=46 equation:

5z^2-9=46

We move all terms to the left:

5z^2-9-(46)=0

We add all the numbers together, and all the variables

5z^2-55=0

a = 5; b = 0; c = -55;
Δ = b2-4ac
Δ = 02-4·5·(-55)
Δ = 1100
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:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{11}}{2*5}=\frac{0-10\sqrt{11}}{10}
=-\frac{10\sqrt{11}}{10}
=-\sqrt{11}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{11}}{2*5}=\frac{0+10\sqrt{11}}{10}
=\frac{10\sqrt{11}}{10}
=\sqrt{11}
$