7v(-6-2v)=12

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Solution for 7v(-6-2v)=12 equation:



7v(-6-2v)=12
We move all terms to the left:
7v(-6-2v)-(12)=0
We add all the numbers together, and all the variables
7v(-2v-6)-12=0
We multiply parentheses
-14v^2-42v-12=0
a = -14; b = -42; c = -12;
Δ = b2-4ac
Δ = -422-4·(-14)·(-12)
Δ = 1092
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$v_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{273}}{2*-14}=\frac{42-2\sqrt{273}}{-28} $
$v_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{273}}{2*-14}=\frac{42+2\sqrt{273}}{-28} $

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