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(8-z)(4z-9)=0
We add all the numbers together, and all the variables
(-1z+8)(4z-9)=0
We multiply parentheses ..
(-4z^2+9z+32z-72)=0
We get rid of parentheses
-4z^2+9z+32z-72=0
We add all the numbers together, and all the variables
-4z^2+41z-72=0
a = -4; b = 41; c = -72;
Δ = b2-4ac
Δ = 412-4·(-4)·(-72)
Δ = 529
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{529}=23$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(41)-23}{2*-4}=\frac{-64}{-8} =+8 $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(41)+23}{2*-4}=\frac{-18}{-8} =2+1/4 $
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