Solve:$ \frac{3 x}{5}+4+x-2=\frac{\frac{3 x}{5} \times x}{2} $

Given:

\( \frac{3 x}{5}+4+x-2=\frac{\frac{3 x}{5} \times x}{2} \)

To do:

We have to solve the given equation.

Solution:

$\frac{3 x}{5}+4+x-2=\frac{\frac{3 x}{5} \times x}{2}$

$\frac{3 x}{5}+x+2=\frac{3 x^2}{10}$
 $\frac{3 x+5x+10}{5}=\frac{3 x^2}{10}$

$8x+10=\frac{3 x^2}{2}$

$2(8x+10)=3x^2$

$3x^2-16x-20=0$

$x=\frac{-(-16) \pm \sqrt{(-16)^2-4(3)(-20)}}{2(3)}$

$x=\frac{16 \pm \sqrt{256+240}}{6}$

$x=\frac{16 \pm \sqrt{496}}{6}$

$x=\frac{16 \pm \sqrt{16\times31}}{6}$

$x=\frac{16 \pm 4\sqrt{31}}{6}$

$x=\frac{8 \pm 2\sqrt{31}}{3}$

$x=\frac{8 + 2\sqrt{31}}{3}$ or $x=\frac{8 - 2\sqrt{31}}{3}$.

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Updated on: 10-Oct-2022

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