# How do you solve #5x^2+2x-3=0# using the quadratic formula?

The solutions are:

The Discriminant is given by:

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To solve the quadratic equation 5x^2 + 2x - 3 = 0 using the quadratic formula, you first identify the coefficients a, b, and c in the general form ax^2 + bx + c = 0. Then, you apply the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a).

In this equation, a = 5, b = 2, and c = -3. Plugging these values into the quadratic formula:

x = (-(2) ± √((2)^2 - 4(5)(-3))) / (2(5)).

Solving inside the square root:

√(2^2 - 4(5)(-3)) = √(4 + 60) = √64 = 8.

Now, substituting this back into the formula:

x = (-(2) ± 8) / (10).

This gives two possible solutions:

x₁ = (-2 + 8) / 10 = 6/10 = 0.6,

x₂ = (-2 - 8) / 10 = -10/10 = -1.

So, the solutions to the quadratic equation 5x^2 + 2x - 3 = 0 are x = 0.6 and x = -1.

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