Question

solve the equation
3 y + 4 / 2 - 6y = -2 / 5​

Answer 1

We have,

$\Large{3y + \frac{4}{2 - 6y} = - \frac{2}{5} }$

$\Rightarrow \Large{ \frac{3y(2 - 6y) + 4}{2 - 6y} = - \frac{2}{5} }$

$\Rightarrow \Large{ \frac{6y - 18 {y}^{2} + 4}{2 - 6y} = - \frac{2}{5} }$

$\Rightarrow \large{ 5(6y - 18 {y}^{2} + 4) = - 2(2 - 6y)}$

$\Rightarrow \large{ 30y - 90 {y}^{2} + 20 = - 4 + 12y}$

$\Rightarrow \large{ 90 {y}^{2} - 18y - 24 = 0}$

This equation is of the form $a {x}^{2} + bx + c = 0$,
where a = 90 , b = - 18 and c = - 24

Thus,
discriminant, D
$= {b}^{2} - 4ac$
$= {( - 18)}^{2} - 4(90)( - 24)$
$= 324 + 8640$
$= 8640 > 0$
Thus, the values of y are real and distinct.

Thus,
$y = \Large{ \frac{ - b \pm \sqrt{D} }{2a} }$

$= \Large{\frac{ - ( - 18) \pm \sqrt{8640} }{2(90)} }$

$= \Large{\frac{18 \: \pm \: 24 \sqrt{15} }{180} }$

$= \Large{\frac{3 \: \pm \: 4 \sqrt{15} }{30} }$

Hence,

$\Large\overline\blue{\fbox{\red{y} = \green{ \frac{3 + 4 \sqrt{15} }{30} }}}$ or $\Large\underline\blue{\fbox{\red{y} = \green{ \frac{3 - 4 \sqrt{15} }{30} }}}$

$\Huge\green{\underline{\fbox{\blue{\star} \: \: \pink{\ddot\smile} \: \: \blue{\star}}}}$
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I hope that .........this answer would help you the best.
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please........mark this answer as ${\fcolorbox{pink}{pink}{Brainliest Answer}}$ .