Solve the following quadratic equations :
(i) $3 (x^{2} - 4) = 5 x$
(ii) x(x + 1) + (x + 2) (x + 3) = 42

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Solution

a) $3 (x^{2} - 4) = 5 x$

Step 1: $3 x^{2} - 5 x - 12 = 0$

$\Rightarrow$ $3 x^{2} - 9 x + 4 x - 12 = 0$

Step 2: 3x(x – 3) + 4(x – 3) = 0

Step 3:(x – 3) (3x + 4) = 0

Step 4: x – 3 = 0 or 3x + 4 = 0

x = 3 or x = – $\frac{4}{3}$

b) x(x + 1) + (x + 2) (x + 3) = 42

Step 1: $x^{2} + x + x^{2} + 3 x + 2 x + 6 - 42 = 0$

Step 2: $2 x^{2} + 6 x - 36 = 0$

Step3: $x^{2} + 3 x - 18 = 0$

$\Rightarrow$ $x^{2} + 6 x - 3 x - 18 = 0$

Step 4: x(x + 6) – 3(x + 6) = 0

Step 5: (x + 6) (x – 3) = 0

$\Rightarrow$ x = – 6 or x = 3.

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Solve the following quadratic equations : (i) 3(x2–4)=5x (ii) x(x + 1) + (x + 2) (x + 3) = 42

Solve the following quadratic equations :
(i) $3 (x^{2} - 4) = 5 x$
(ii) x(x + 1) + (x + 2) (x + 3) = 42