Solve the Quadratic Equation by Factorization: 3x² − 14x − 5 = 0

Question: Solve the following quadratic equation by factorization:

$$ 3x^2-14x-5=0 $$

Solution

$$ 3x^2-15x+x-5=0 $$

$$ 3x(x-5)+1(x-5)=0 $$

$$ (x-5)(3x+1)=0 $$

Either

$$ x-5=0 $$

$$ x=5 $$

or

$$ 3x+1=0 $$

$$ x=-\frac{1}{3} $$

Hence,

$$ \boxed{x=5,\ -\frac{1}{3}} $$