Solve 3

Solve quadratic equation:

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

Correct result:

n1 =  0.271
n2 =  -0.176

Solution:

(6n+1)(4n−1)=3n2  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±0.22335313142 n1=0.270972179039 n2=−0.175734083801   Factored form of the equation:  21(n−0.270972179039)(n+0.175734083801)=0  n1=0.271(6n+1) (4n-1)=3n^2 \ \\ \ \\ 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 0.22335313142 \ \\ n_{1}=0.270972179039 \ \\ n_{2}=-0.175734083801 \ \\ \ \\ \text{ Factored form of the equation: } \ \\ 21 (n -0.270972179039) (n +0.175734083801)=0 \ \\ \ \\ n_{1}=0.271

Checkout calculation with our calculator of quadratic equations.

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

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