2z(z-1)=5z2-7

Solution for 2z(z-1)=5z2-7 equation:

2z(z-1)=5z^2-7

We move all terms to the left:

2z(z-1)-(5z^2-7)=0

We multiply parentheses

2z^2-2z-(5z^2-7)=0

We get rid of parentheses

2z^2-5z^2-2z+7=0

We add all the numbers together, and all the variables

-3z^2-2z+7=0

a = -3; b = -2; c = +7;
Δ = b2-4ac
Δ = -22-4·(-3)·7
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{22}}{2*-3}=\frac{2-2\sqrt{22}}{-6}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{22}}{2*-3}=\frac{2+2\sqrt{22}}{-6}
$