5x=2x^2-3

Answer 1

To solve for x in the equation 5x = 2x^2 - 3, we first need to rearrange the equation to set it equal to zero:

2x^2 - 5x - 3 = 0

Next, we can use the quadratic formula to solve for x:

x = (-(-5) ± sqrt((-5)^2 - 4(2)(-3))) / 2(2)
x = (5 ± sqrt(25 + 24)) / 4
x = (5 ± sqrt(49)) / 4
x = (5 ± 7) / 4

This gives us two possible solutions for x:

x = (5 + 7) / 4 = 12 / 4 = 3
x = (5 - 7) / 4 = -2 / 4 = -0.5

Therefore, the solutions for x are x = 3 and x = -0.5.