Question

Solve by using the Quadratic Formula:$3y(y-2)-3=0$

Short answer

The solution of the above equation is$y=1$

Step-by-step solution

Given information

We are given a quadratic equation$3y(y-2)-3=0$

Distribute and write the equation in standard form

On distributing we get

$3y^2-6y-3=0$

Identify the values of a,b,cand write the quadratic formula

On comparing with standard equation we get $a=3,y=-6,c=-3$

The quadratic formula can be given as

$y=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Substitute the values in the quadratic formula and simplify

On substituting we get

$$\begin{gathered} y=\frac{6\pm \sqrt{36-4\left(3\right)(-3)}}{2\left(3\right)} \\ y=\frac{6\pm \sqrt{36+36}}{6} \\ y=\frac{6\pm \sqrt{72}}{6} \\ y=\frac{6\pm 6\sqrt{2}}{6} \end{gathered}$$

Find the common factor and remove it

Now we take out the common factor we get

$$\begin{gathered} y=\frac{6(1\pm \sqrt{2})}{6} \\ y=1\pm \sqrt{2} \end{gathered}$$

Conclusion

The solution of the quadratic equation is$y=1\pm \sqrt{2}$