(4z-10)z=-5

Solution for (4z-10)z=-5 equation:

(4z-10)z=-5

We move all terms to the left:

(4z-10)z-(-5)=0

We add all the numbers together, and all the variables

(4z-10)z+5=0

We multiply parentheses

4z^2-10z+5=0

a = 4; b = -10; c = +5;
Δ = b2-4ac
Δ = -102-4·4·5
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{5}}{2*4}=\frac{10-2\sqrt{5}}{8}
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{5}}{2*4}=\frac{10+2\sqrt{5}}{8}
$