Given,
⇒ 2 5 x 2 − 3 x − 5 = 0 ⇒ 2 5 x 2 − 5 x + 2 x − 5 = 0 ⇒ 5 x ( 2 x − 5 ) + 1 ( 2 x − 5 ) = 0 ⇒ ( 5 x + 1 ) ( 2 x − 5 ) = 0 ⇒ ( 5 x + 1 ) = 0 or ( 2 x − 5 ) = 0 [Using Zero-product rule] ⇒ ( 5 x + 1 ) = 0 or ( 2 x − 5 ) = 0 ⇒ 5 x = − 1 or 2 x = 5 ⇒ x = − 1 5 or x = 5 2 . \Rightarrow 2\sqrt{5}x^2 - 3x - \sqrt{5} = 0 \\[1em] \Rightarrow 2\sqrt{5}x^2 - 5x + 2x - \sqrt{5} = 0 \\[1em] \Rightarrow \sqrt{5}x(2x - \sqrt{5}) + 1(2x - \sqrt{5}) = 0 \\[1em] \Rightarrow (\sqrt{5}x + 1)(2x - \sqrt{5}) = 0 \\[1em] \Rightarrow (\sqrt{5}x + 1)= 0 \text{ or } (2x - \sqrt{5}) = 0 \text{ [Using Zero-product rule] } \\[1em] \Rightarrow (\sqrt{5}x + 1)= 0 \text{ or } (2x - \sqrt{5}) = 0 \\[1em] \Rightarrow \sqrt{5}x = -1 \text{ or } 2x = \sqrt{5} \\[1em] \Rightarrow x = \dfrac{-1}{\sqrt{5}} \text{ or } x = \dfrac{\sqrt{5}}{2}. ⇒ 2 5 x 2 − 3 x − 5 = 0 ⇒ 2 5 x 2 − 5 x + 2 x − 5 = 0 ⇒ 5 x ( 2 x − 5 ) + 1 ( 2 x − 5 ) = 0 ⇒ ( 5 x + 1 ) ( 2 x − 5 ) = 0 ⇒ ( 5 x + 1 ) = 0 or ( 2 x − 5 ) = 0 [Using Zero-product rule] ⇒ ( 5 x + 1 ) = 0 or ( 2 x − 5 ) = 0 ⇒ 5 x = − 1 or 2 x = 5 ⇒ x = 5 − 1 or x = 2 5 .
Hence, x = { 5 2 , − 1 5 } x = \Big{\dfrac{\sqrt{5}}{2}, \dfrac{-1}{\sqrt{5}}\Big} x = { 2 5 , 5 − 1 }
