Question

In the following exercises, solve by using the Quadratic Formula.

$7y^2+4y-3=0$

Short answer

The solutions are$y=-1andy=\frac{3}{7}.$

Step-by-step solution

Given information.

The given information is$7y^2+4y-3=0$

Use the quadratic formula.

The quadratic formula for the equation $a{x}^2+bx+c=0$is $y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Now we compare the given equation with the standard form we get$a=7,b=4andc=-3.$

Now we substitute these values in the quadratic formula.

localid="1653585740555" $$\begin{gathered} x=\frac{-4\pm \sqrt{\left(4^2\right)-4\left(7\right)\left(-3\right)}}{2\left(7\right)} \\ y=\frac{-4\pm \sqrt{16+84}}{14} \\ y=\frac{-4\pm \sqrt{100}}{14} \\ y=\frac{-4\pm 10}{14} \end{gathered}$$

The two equations arelocalid="1653585775380" $y=\frac{-4+10}{14}andy=\frac{-4-10}{14}.$

Solve both the equations for x.

$$\begin{gathered} y=\frac{-4+10}{14} \\ y=\frac{6}{14} \\ y=\frac{3}{7} \\ Or \\ y=\frac{-4-10}{14} \\ y=\frac{-14}{-14} \\ y=-1 \end{gathered}$$

Therefore, the two solutions are$y=-1andy=\frac{3}{7}.$