# Math Help - Solve for x

1. ## Solve for x

21x^2 - 83x + 34 = 0

i know i will get two values of ex by factorization. but i am not being able to middle term factorize it.

3. Originally Posted by saha.subham
21x^2 - 83x + 34 = 0

i know i will get two values of ex by factorization. but i am not being able to middle term factorize it.
It's not factorable. For it to be factorable over the integers the discriminant would need to be a perfect square.
\begin{aligned}
b^2 - 4ac &= (-83)^2 - 4(21)34 \\
&= 6889 - 2856 \\
&= 4033
\end{aligned}

... and 4033 is not a perfect square.

4. Relatively few quadratics can be factored with integer coefficients. "Complete the square" or use the quadratic formula instead.

if $ax^2+bx+c=0$
then $x=\frac{-b\pm \sqrt{(b^2-4ac)}}{2a}$