Question

2/3(3x-2)=4/5(2x-3)-4/3​

Answer 1

$\huge\bold{\color{aqua}{Solution :-}}$

$\quad\bold{\frac{2}{3(3x-2)}=\frac{4}{5(2x-3)}-\frac{4}{3}}$

$\Rightarrow\bold{\frac{2}{3(3x-2)}=\frac{4}{10x-15)}-\frac{4}{3}}$

$\Rightarrow\bold{\frac{2}{3(3x-2)}=\frac{(4×3)-4(10x-15)}{3(10x-15)}}$

$\Rightarrow\bold{\frac{2}{\red{\cancel{\blue{3}}}(3x-2)}=\frac{12-40x+60)}{\red{\cancel{\blue{3}}}(10x-15)}}$

$\Rightarrow\bold{\frac{2}{3x-2}=\frac{-40x+72}{10x-15}}$

$\Rightarrow\bold{\frac{2}{3x-2}=\frac{4(-10x+18)}{10x-15}}$

$\Rightarrow\bold{\frac{\red{\cancel{\blue{\:2}}}}{3x-2}=\frac{\red{\cancel{\blue{\:4}}}^{\green{\:2}}(-10x+18)}{10x-15}}$

$\Rightarrow\bold{\frac{1}{3x-2}=\frac{2(-10x+18)}{10x-15}}$

$\Rightarrow\bold{10x-15=2(-10x+18)(3x-2)}$

$\Rightarrow\bold{10x-15=2(-30x²+20x+54x-36)}$

$\Rightarrow\bold{10x-15=2(-30x²+74x-36)}$

$\Rightarrow\bold{10x-15=-60x²+148x-72}$

$\Rightarrow\bold{10x-15+60x²-148x+72=0}$

$\Rightarrow\bold{60x²-138x+57=0}$

$\Rightarrow\bold{3(20x²-46x+19)=0}$

$\Rightarrow\bold{20x²-46x+19=\frac{0}{3}}$

$\Rightarrow\bold{20x²-46x+19=0}$

$\bold{\purple{\text{Here}}}$

$\quad\bf\bold{\text{a=20 ; b=-46 ; c=19}}$

$\bold{\purple{\text{Now will use the quadratic formula}}}$

$\quad\bold{\blue{x}=\orange{\frac{-b\pm\sqrt{b²-4ac}}{2a}}}$

$\bold{\purple{\text{On substituting the values}}}$

$\Rightarrow\bold{x=\frac{-(-46)\pm\sqrt{(-46)²-4(20)(19)}}{2(20)}}$

$\Rightarrow\bold{x=\frac{46\pm\sqrt{2116-80(19)}}{40}}$

$\Rightarrow\bold{x=\frac{46\pm\sqrt{2116-1520}}{40}}$

$\Rightarrow\green{\boxed{\bold{\red{x}=\pink{\frac{46\pm\sqrt{596}}{40}}}}}$