The given equation is -2x^2 + 7x = 3.
To solve this equation using the quadratic formula, we first need to write it in standard form: ax^2 + bx + c = 0. So we rearrange the equation:
-2x^2 + 7x - 3 = 0
Now we can identify the coefficients:
a = -2, b = 7, c = -3
The quadratic formula is:
x = (-b ± sqrt(b^2 - 4ac)) / 2a
Substituting the values, we get:
x = (-7 ± sqrt(7^2 - 4(-2)(-3))) / 2(-2)
Simplifying the expression, we get:
x = (-7 ± sqrt(49 - 24)) / (-4)
x = (-7 ± sqrt(25)) / (-4)
We take the positive and negative values of the square root separately:
x = (-7 + 5) / (-4) or x = (-7 - 5) / (-4)
Simplifying each expression, we get:
x = -1/2 or x = 3
Therefore, the solutions to the equation -2x^2 + 7x = 3 are x = -1/2 and x = 3.