Two quadratic equations with the formula

Statement

Solve using the quadratic formula:

• (a) $3x^2-7x+2=0$
• (b) $2x^2+5x-12=0$

Solution

(a) $\Delta=49-24=25$, $x=\dfrac{7\pm 5}{6}$, so $x=2$ or $x=\dfrac13$.

(b) $\Delta=25+96=121$, $x=\dfrac{-5\pm 11}{4}$, so $x=\dfrac32$ or $x=-4$.

$\boxed{x_a=2,\ \tfrac13;\qquad x_b=\tfrac32,\ -4}$