Question

Solve Quadratic : x/3+3/(6-x)=2(6+x)/15​

Answer 1

Answer:

$\normalsize x = 9 \: \: \: \: \: , \: \: \: x = 1$

Step-by-step explanation:

$→\Large\frac{x}{3} + \frac{3}{6 - x} = \frac{2(6 + x)}{15}$

$→ \Large \frac{x(6 - x ) + 3 \times 3}{3(6 - x)} = \frac{12 + 2x}{15}$

$→ \Large \frac{6x - {x}^{2} + 9 }{18 - 3x} = \frac{12 + 2x}{15}$

$→ \normalsize( { - x}^{2} + 6x + 9)15 = (2x + 12)(18 - 3x)$

$→ \normalsize - 15 {x}^{2} + 90x + 135 = 36 x - 6 {x}^{2} + 216 - 36x$

$→\normalsize - 15 {x}^{2} + 90x + 135 = - 6 {x}^{2} + 216$

$→ \normalsize - 15 {x}^{2} + 90x + 135 + 6 {x}^{2} - 216 = 0$

$→ \normalsize - 9 {x}^{2} + 90x - 81 = 0$

$→\normalsize - 9( {x}^{2} - 10x + 9) = 0$

$→ \normalsize {x}^{2} - 10x + 9 = \frac{0}{ - 9}$

$→\normalsize {x}^{2} - 10x + 9 = 0$

$→\normalsize {x}^{2} - x - 9x + 9 = 0$

$→\normalsize x(x - 1) - 9(x - 1) = 0$

$→\normalsize (x - 9)(x - 1) = 0$

$→ \large \bf \green{ \boxed { x = 9 \: \: \: \: \: , \: \: \: x = 1}}$