Question

Solve the following quadratic equation by using formula method
$3y^2+7y+4=0$

Answer 1

The given quadratic equation is
$3y^2+7y+4=0$
Comparing this with $a{x}^2+bx+c=0$
Here, $a=3,b=7,c=4$
$\therefore y=\frac{-b\pm \sqrt{b^2}-4ac}{2a}$
$=\frac{-7\pm \sqrt{\left(7^2\right)-4\times 3\times 4}}{2\left(3\right)}$
$=\frac{-7\pm \sqrt{49-48}}{6}=\frac{-7\pm \sqrt{1}}{6}=\frac{-7\pm 1}{6}$
$\therefore y=\frac{-7+1}{6}$ or $y=\frac{-7-1}{6}$
$\therefore y=\frac{-6}{6}$ or $y=-\frac{8}{6}$
$\therefore y=-1$ or $y-\frac{4}{3}$