Final answer:
To find the exact solutions to the equation -(3)/(4)x²3x=-9, we can rearrange it into the quadratic equation form and use the quadratic formula to solve for x.
Step-by-step explanation:
To find the exact solutions to the equation -(3)/(4)x²3x=-9, we can rearrange it into the quadratic equation form ax² + bx + c = 0. In this case, a = -(3)/(4), b = 3, and c = -9. Then, we can use the quadratic formula x = (-b ± √(b² - 4ac))/(2a) to solve for the two possible values of x.
Substituting the values, we get x = (-3 ± √(3² - 4*(-(3)/(4))*(-9)))/(2*(-(3)/(4))). Simplifying further, x = (-3 ± √(9 - 27/4))/(-(6/4)). Continuing to simplify, x = (-3 ± √(-9/4))/(-(6/4)).
Finally, we can simplify the expression by multiplying the numerator and denominator by 4 to eliminate the fractions. So, x = (-12 ± √(-9))/(6). The square root of a negative number is an imaginary number, so x = (-12 ± 3i)/6. This can also be written as x = -2 ± (1/2)i.