Question

solve for x:



x^+5x+8 / 5x^+6x+12 =14/13​

Answer 1

ANSWER:

Given:

• (x² + 5x + 8)/(5x² + 6x + 12) = 14/13

To Find:

• The value of x

Solution:

We are given that,

$\implies\dfrac{x^2+5x+8}{5x^2+6x+12}=\dfrac{14}{13}$

So, on cross-multiplying,

$\implies13(x^2+5x+8)=14(5x^2+6x+12)$

Solving brackets,

$\implies13x^2+65x+104=70x^2+84x+168$

Transposing all terms in LHS to RHS,

$\implies0=70x^2+84x+168-(13x^2+65x+104)$

So,

$\implies0=70x^2+84x+168-13x^2-65x-104$

Solving like terms,

$\implies0=57x^2+19x+64$

So,

$\implies57x^2+19x+64=0$

Now, applying Quadratic Formula,

$\hookrightarrow x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a = 57, b = 19 and c = 64.

So,

$\implies x=\dfrac{-(19)\pm\sqrt{(19)^2-4(57)(64)}}{2(57)}$

So,

$\implies x=\dfrac{-19\pm\sqrt{361-14592}}{114}$

So,

$\implies x=\dfrac{-19\pm\sqrt{-14231}}{114}$

Hence,

$\implies x=\dfrac{-19\pm\sqrt{14231}i}{114}$

Therefore,

$\implies\bf x=\dfrac{-19+\sqrt{14231}i}{114}\,,\:\dfrac{-19-\sqrt{14231}i}{114}\,$

Answer 2

Answer:

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