Question 3 of 10, Step 1 of 1
Solve the following quadratic equation using the quadratic formula.

Question

Question 3 of 10, Step 1 of 1 Solve the following quadratic equation using the quadratic formula. $$ -4 y^{2}-3 y+4=0 $$

UpStudy AI · Accepted Answer

We start with the quadratic equation

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

It is often easier to work with a positive leading coefficient. Multiply both sides of the equation by $$-1$$:

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

Now the equation is in standard form

$$
ay^2 + by + c = 0,
$$

with

$$
a = 4,\quad b = 3,\quad c = -4.
$$

The quadratic formula is

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

Substitute the values of $$a$$, $$b$$, and $$c$$ into the formula:

$$
y = \frac{-3 \pm \sqrt{3^2 - 4 \cdot 4 \cdot (-4)}}{2 \cdot 4}.
$$

Calculate the discriminant:

$$
3^2 - 4 \cdot 4 \cdot (-4) = 9 + 64 = 73.
$$

Thus, the solutions become

$$
y = \frac{-3 \pm \sqrt{73}}{8}.
$$

These are the solutions of the quadratic equation.
The solutions are $$ y = \frac{-3 + \sqrt{73}}{8} $$ and $$ y = \frac{-3 - \sqrt{73}}{8} $$.

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