E1 - Quadratic equations - Immediate

Examples : $16x^2-9=0;\left(-2x+4\right)\left(5x-1\right)=0;{\left(5x-2\right)}^2=0$        

E2 - Quadratic equations- Immediate

Examples : $\frac{x^2}{4}=16;\left(\frac{x}{3}-4\right)\left(3x+\frac{4}{3}\right)=0;{\left(\frac{x}{2}-5\right)}^2=0$

E3 - Quadratic equations - Factorization

Examples : $x^2-9-\left(5x+2\right)\left(x-3\right)=0;\left(3x+2\right)\left(x-3\right)+\left(x-4\right)\left(x-3\right)=0$

E4 - Quadratic equations - Factorization

Examples : $4x^2+12x+9+\left(x-4\right)\left(2x+3\right)=0;\left(4x+4\right)\left(-4x+12\right)+\left(-x+3\right)\left(x-4\right)=0$

E5 - Quadratic equations - Discriminant

Examples : $x^2-3x+4=0;-2x^2+2x+1=0;x^2+2x+1=0$

E6 - Quadratic equations - Discriminant

Examples :   $-x^2+\frac{4}{5}x-4=0;4x^2+\frac{2}{5}x+\frac{3}{5}=0$

E7 - Quadratic equations - Calculations and discriminant

Examples :   $\left(4x+2\right)\left(3x-6\right)=3x\left(6x-3\right);-2x^2-x+3=4x^2+4x+2$

E8 - Quadratic equations - Calculations and discriminant  

Examples : ${\left(4x+5\right)}^2={\left(5x-1\right)}^2;{\left(2x+2\right)}^2-\left(3x-2\right)\left(4x-1\right)=0$

E9 - Fractional equations transforming into quadratic equations  

Example : $\frac{1}{x+3}+\frac{1}{x-1}=\frac{2}{x};\frac{2x+3}{-3x-1}=\frac{4x-1}{2x-1}$