4z-3-(9-2z)z=-5

Solution for 4z-3-(9-2z)z=-5 equation:

4z-3-(9-2z)z=-5

We move all terms to the left:

4z-3-(9-2z)z-(-5)=0

We add all the numbers together, and all the variables

4z-(-2z+9)z-3-(-5)=0

We add all the numbers together, and all the variables

4z-(-2z+9)z+2=0

We multiply parentheses

2z^2+4z-9z+2=0

We add all the numbers together, and all the variables

2z^2-5z+2=0

a = 2; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·2·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*2}=\frac{2}{4}
=1/2
$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*2}=\frac{8}{4}
=2
$