4xsquared+ 4x -3 =0

SOLVE

4x^2 + 4x - 3 = 0

it factors
(2x+3)(2x-1) = 0
so x = -3/2 or x = 1/2

To solve the equation 4x^2 + 4x - 3 = 0, you can use the quadratic formula or factorization. Let's solve it using the quadratic formula.

Step 1: Identify the coefficients in the equation.
a = 4, b = 4, c = -3

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

Step 3: Substitute the values of a, b, and c into the formula:
x = (-4 ± √(4^2 - 4*4*(-3))) / (2*4)

Step 4: Simplify the equation:
x = (-4 ± √(16 + 48)) / 8
x = (-4 ± √64) / 8
x = (-4 ± 8) / 8

Step 5: Evaluate both possible solutions:
x1 = (-4 + 8) / 8
x1 = 4 / 8
x1 = 1/2

x2 = (-4 - 8) / 8
x2 = -12 / 8
x2 = -3/2

Therefore, the solutions to the equation 4x^2 + 4x - 3 = 0 are x = 1/2 and x = -3/2.

To solve the quadratic equation 4x^2 + 4x - 3 = 0, we can use the quadratic formula. The quadratic formula is used to solve any quadratic equation ax^2 + bx + c = 0, where a, b, and c are coefficients.

The quadratic formula states that for an equation of the form ax^2 + bx + c = 0, the solutions for x can be found using the formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In our case, a = 4, b = 4, and c = -3. We can substitute these values into the quadratic formula:

x = (-4 ± √(4^2 - 4*4*(-3))) / (2*4)

Simplifying further:

x = (-4 ± √(16 + 48)) / 8
x = (-4 ± √64) / 8
x = (-4 ± 8) / 8

This gives us two possible solutions:
1. x = (-4 + 8) / 8 = 4 / 8 = 0.5
2. x = (-4 - 8) / 8 = -12 / 8 = -1.5

Therefore, the solutions to the equation 4x^2 + 4x - 3 = 0 are x = 0.5 and x = -1.5.