Solve 3

Solve quadratic equation:

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

Result

n1 =  0.271
n2 =  -0.176

Solution:

 21n2−2n−1=0  a=21;b=−2;c=−1 D=b2−4ac=22−4⋅21⋅(−1)=88 D>0  n1,2=−b±D2a=2±8842=2±22242 n1,2=0.04761905±0.22335313142016 n1=0.27097217903921 n2=−0.17573408380112   Factored form of the equation:  21(n−0.27097217903921)(n+0.17573408380112)=0  n1=0.271≐0.271=0.271 \ \\ 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.

n2=(−0.1757)≐−0.1757=−0.176n_{2}=(-0.1757) \doteq -0.1757=-0.176

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