(6+z)(3z+7)=0

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Solution for (6+z)(3z+7)=0 equation:



(6+z)(3z+7)=0
We add all the numbers together, and all the variables
(z+6)(3z+7)=0
We multiply parentheses ..
(+3z^2+7z+18z+42)=0
We get rid of parentheses
3z^2+7z+18z+42=0
We add all the numbers together, and all the variables
3z^2+25z+42=0
a = 3; b = 25; c = +42;
Δ = b2-4ac
Δ = 252-4·3·42
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$z_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-11}{2*3}=\frac{-36}{6} =-6 $
$z_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+11}{2*3}=\frac{-14}{6} =-2+1/3 $

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