6z^2-31z+5=0

Solution for 6z^2-31z+5=0 equation:

6z^2-31z+5=0

a = 6; b = -31; c = +5;
Δ = b2-4ac
Δ = -312-4·6·5
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-29}{2*6}=\frac{2}{12}
=1/6
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+29}{2*6}=\frac{60}{12}
=5
$