2z(2)-3(2)-10=2z

Solution for 2z(2)-3(2)-10=2z equation:

2z(2)-3(2)-10=2z

We move all terms to the left:

2z(2)-3(2)-10-(2z)=0

We add all the numbers together, and all the variables

2z^2-2z-42=0

a = 2; b = -2; c = -42;
Δ = b2-4ac
Δ = -22-4·2·(-42)
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{85}}{2*2}=\frac{2-2\sqrt{85}}{4}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{85}}{2*2}=\frac{2+2\sqrt{85}}{4}
$