二次方程式計算機

Your input: solve the quadratic equation $$$y^{2} - 20 y + 64 = 0$$$ by using quadratic formula.

The standard quadratic equation has the form $$$ay^2+by+c=0$$$.

In our case, $$$a=1$$$, $$$b=-20$$$, $$$c=64$$$.

Now, find the discriminant using the formula $$$D=b^2-4ac$$$: $$$D=\left(-20\right)^2-4\cdot 1 \cdot 64=144$$$.

Find the roots of the equation using the formulas $$$y_1=\frac{-b-\sqrt{D}}{2a}$$$ and $$$y_2=\frac{-b+\sqrt{D}}{2a}$$$

$$$y_1=\frac{-\left(-20\right)-\sqrt{144}}{2\cdot 1}=4$$$ and $$$y_2=\frac{-\left(-20\right)+\sqrt{144}}{2\cdot 1}=16$$$

Answer: $$$y_1=4$$$; $$$y_2=16$$$