5z2=-2+9z

Solution for 5z2=-2+9z equation:

5z^2=-2+9z

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

5z^2-9z+2=0

a = 5; b = -9; c = +2;
Δ = b2-4ac
Δ = -92-4·5·2
Δ = 41
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{-(-9)-\sqrt{41}}{2*5}=\frac{9-\sqrt{41}}{10}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{41}}{2*5}=\frac{9+\sqrt{41}}{10}
$