Solve 3

Solve quadratic equation:

(6n+1) (4n-1) = 3n²

Correct answer:

n₁ =  0.271
n₂ =  -0.1757

Step-by-step explanation:

$$\begin{gathered} (6n+1)(4n-1)=3n^2 \\ 21n^2-2n-1=0 \\ a=21;b=-2;c=-1 \\ D=b^2-4ac=2^2-4\cdot 21\cdot (-1)=88 \\ D>0 \\ {n}_{1,2}={\displaystyle \frac{-b\pm \sqrt{D}}{2a}}={\displaystyle \frac{2\pm \sqrt{88}}{42}}={\displaystyle \frac{2\pm 2\sqrt{22}}{42}} \\ {n}_{1,2}=0.04761905\pm 0.22335313142 \\ {n}_1=0.270972179039 \\ {n}_2=-0.175734083801 \\ \text{ Factored form of the equation: } \\ 21(n-0.270972179039)(n+0.175734083801)=0 \\ {n}_1=0.271=0.271 \end{gathered}$$

Our quadratic equation calculator calculates it.

$n_2=(-0.1757)=-0.1757$

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