Solve for x :

Given equation: 2x² + √3 x – 3 = 0

_{Comparing above equation with ax}² + bx + c = 0,

_{⇒ a = 2; b = √3; c = -3}

_{Now, b}² – 4ac = (√3)² – 4(2)(-3)

_{= 3 – (-24)}

_{⇒ b}² – 4ac = 27 ≥ 0

_{We know that, if b}² – 4ac ≥ 0 then the roots of the quadratic equation ax² + bx + c = 0 is given by _{[–b (√b}²– 4ac)] / 2a which is known as the quadratic formula.

_{⇒ x = [-√3 √27]/ 2(2)}

_{⇒ x = [-√3 3√3] / 4}

_{⇒ x = [-√3 + 3√3] / 4 (or) x = [-√3 - 3√3] / 4}

⇒ x = (2√3)/4 (or) x = (-4√3)/4

⇒ x = √3/2 (or) x = -√3

Ans. The solutions of x are √3/2 (or) x = -√3.