Solve the following equation by the quadratic formula: \(7{x^2}+16x+9=0\)

Solve the following equation by the quadratic formula: \(5{z^2}+18z+13=0\)

Solve by factorising: \(\dfrac{{x+3}}{{2x-7}}=\dfrac{{2x-1}}{{x-3}}\)

Amy's mother is 2 years less than 5 times Amy's age. 12 years from now, the product of their ages will be 1230. What is Amy's present age?

As shown in figure, ABC is a right angles triangle with dimensions marked in cm. If its area is \(60~\text{cm}^2\), find the length of its hypotenuse AC.

Solve by factoring: \(x=\dfrac{{5x-6}}{x}\)

Solve by factorising: \(x+\dfrac{3}{x}=-4\)

ABCD is a kite such that its longer diagonal is 10 cm longer than twice the length of diagonal BD. If its area is \(300~\text{cm}^2\). find the length of longer diagonal.

The solutions to \({(2x + 1)^2} = 49\) are?

The solutions to \(3x + 5 = \dfrac{2}{x}\) are?

Solve \(x - 2 = \dfrac{8}{x}\)

The solutions to \(2x^2 + x - 3=0\) are?

The solutions to \(x + \dfrac{2}{x}\) = \(\dfrac{9}{2}\) are? 

The solutions to \({(x - 7)^2} = 64\) are?

The solutions to \(x = {\rm{1 + }}\dfrac{1}{x}\) are? 

A rectangular garden, 7m by 3m is surrounded by a concrete path of unitform width. If the area of the path is \({\rm{39}}{{\rm{m}}^3}\), then the width is?