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(8+z)(4z-1)=8
We move all terms to the left:
(8+z)(4z-1)-(8)=0
We add all the numbers together, and all the variables
(z+8)(4z-1)-8=0
We multiply parentheses ..
(+4z^2-1z+32z-8)-8=0
We get rid of parentheses
4z^2-1z+32z-8-8=0
We add all the numbers together, and all the variables
4z^2+31z-16=0
a = 4; b = 31; c = -16;
Δ = b2-4ac
Δ = 312-4·4·(-16)
Δ = 1217
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}$$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-\sqrt{1217}}{2*4}=\frac{-31-\sqrt{1217}}{8} $$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{1217}}{2*4}=\frac{-31+\sqrt{1217}}{8} $
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