# Solve 3

(6n+1) (4n-1) = 3n2

Result

n1 =  0.271
n2 =  -0.176

#### Solution:

$\ \\ 21n^2 -2n -1=0 \ \\ \ \\ a=21; b=-2; c=-1 \ \\ D=b^2 - 4ac=2^2 - 4\cdot 21 \cdot (-1)=88 \ \\ D>0 \ \\ \ \\ n_{1,2}=\dfrac{ -b \pm \sqrt{ D } }{ 2a }=\dfrac{ 2 \pm \sqrt{ 88 } }{ 42 }=\dfrac{ 2 \pm 2 \sqrt{ 22 } }{ 42 } \ \\ n_{1,2}=0.04761905 \pm 0.22335313142016 \ \\ n_{1}=0.27097217903921 \ \\ n_{2}=-0.17573408380112 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 21 (n -0.27097217903921) (n +0.17573408380112)=0 \ \\ \ \\ n_{1}=0.271 \doteq 0.271=0.271$

Checkout calculation with our calculator of quadratic equations.

$n_{2}=(-0.1757) \doteq -0.1757=-0.176$

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