(2)/(3)x^2+x=(1)/(2)

Question

how do i solve this

Answer 1

2/3x^2 + x = 1/2  multiply everthing by 6 to get rid of the denominators

4x^2 +6x = 3

4x^2 + 6x - 3 = 0  use quadratic equation

a = 4, b = 6, c = -3

[-b +or- sqrt(b^2 - 4ac)]/2a

[-6 +or- sqrt(6^2 - 4*4*(-3)]/2*4

[-6 +or- sqrt(36 + 48)]/8

[-6 +or- sqrt(84)]/8

[-6 +or- 2*sqrt(21)]/8

[-3 +or- sqrt(21)]/ 4  reduce by 2