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(1+z)(4z+7)=0
We add all the numbers together, and all the variables
(z+1)(4z+7)=0
We multiply parentheses ..
(+4z^2+7z+4z+7)=0
We get rid of parentheses
4z^2+7z+4z+7=0
We add all the numbers together, and all the variables
4z^2+11z+7=0
a = 4; b = 11; c = +7;
Δ = b2-4ac
Δ = 112-4·4·7
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$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3}{2*4}=\frac{-14}{8} =-1+3/4 $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3}{2*4}=\frac{-8}{8} =-1 $
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