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(5z-6)(2+z)=0
We add all the numbers together, and all the variables
(5z-6)(z+2)=0
We multiply parentheses ..
(+5z^2+10z-6z-12)=0
We get rid of parentheses
5z^2+10z-6z-12=0
We add all the numbers together, and all the variables
5z^2+4z-12=0
a = 5; b = 4; c = -12;
Δ = b2-4ac
Δ = 42-4·5·(-12)
Δ = 256
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{256}=16$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*5}=\frac{-20}{10} =-2 $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*5}=\frac{12}{10} =1+1/5 $
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