90z^2-33z+3=0

Solution for 90z^2-33z+3=0 equation:

90z^2-33z+3=0

a = 90; b = -33; c = +3;
Δ = b2-4ac
Δ = -332-4·90·3
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-33)-3}{2*90}=\frac{30}{180}
=1/6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-33)+3}{2*90}=\frac{36}{180}
=1/5
$