7(3n+8)(8n-3)=0

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Solution for 7(3n+8)(8n-3)=0 equation:



7(3n+8)(8n-3)=0
We multiply parentheses ..
7(+24n^2-9n+64n-24)=0
We multiply parentheses
168n^2-63n+448n-168=0
We add all the numbers together, and all the variables
168n^2+385n-168=0
a = 168; b = 385; c = -168;
Δ = b2-4ac
Δ = 3852-4·168·(-168)
Δ = 261121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{261121}=511$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(385)-511}{2*168}=\frac{-896}{336} =-2+2/3 $
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(385)+511}{2*168}=\frac{126}{336} =3/8 $

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