2z^2-30z+20=0

Solution for 2z^2-30z+20=0 equation:

2z^2-30z+20=0

a = 2; b = -30; c = +20;
Δ = b2-4ac
Δ = -302-4·2·20
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{185}}{2*2}=\frac{30-2\sqrt{185}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{185}}{2*2}=\frac{30+2\sqrt{185}}{4}
$