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Your input: solve the quadratic equation $$$4 y^{2} - 5 y - 6 = 0$$$ by using quadratic formula.

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

In our case, $$$a=4$$$, $$$b=-5$$$, $$$c=-6$$$.

Now, find the discriminant using the formula $$$D=b^2-4ac$$$: $$$D=\left(-5\right)^2-4\cdot 4 \cdot \left(-6\right)=121$$$.

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

$$$y_1=\frac{-\left(-5\right)-\sqrt{121}}{2\cdot 4}=- \frac{3}{4}$$$ and $$$y_2=\frac{-\left(-5\right)+\sqrt{121}}{2\cdot 4}=2$$$

Answer: $$$y_1=- \frac{3}{4}$$$; $$$y_2=2$$$