solve using the quadratic formula

2x^2 +6x-3=0

To solve the quadratic equation 2x^2 + 6x - 3 = 0 using the quadratic formula, you need to follow these steps:

Step 1: Identify the values of coefficients a, b, and c from the equation.
In this case, a = 2, b = 6, and c = -3.

Step 2: Use the quadratic formula, which states that for any quadratic equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)

Step 3: Plug in the values of a, b, and c into the quadratic formula.
x = (-(6) ± √((6)^2 - 4(2)(-3))) / (2(2))

Step 4: Simplify the expression inside the square root and perform the calculations.
x = (-6 ± √(36 + 24)) / 4
= (-6 ± √60) / 4

Step 5: Further simplify the expression if possible.
x = (-6 ± √(4 * 15)) / 4
= (-6 ± 2√15) / 4

Step 6: Divide both the numerator and denominator by 2.
x = -3 ± √15 / 2

Therefore, the solutions to the quadratic equation 2x^2 + 6x - 3 = 0, using the quadratic formula, are:
x = (-3 + √15) / 2
x = (-3 - √15) / 2