Solve x-4/3x^2-75

Evaluate

x - \frac{4}{3} x^{2} - 75

To find the roots of the expression,set the expression equal to 0

x - \frac{4}{3} x^{2} - 75 = 0

Rewrite in standard form

- \frac{4}{3} x^{2} + x - 75 = 0

Multiply both sides

\frac{4}{3} x^{2} - x + 75 = 0

Multiply both sides

3 (\frac{4}{3} x^{2} - x + 75) = 3 \times 0

Calculate

4 x^{2} - 3 x + 225 = 0

Substitute a= 4,b= - 3 and c= 225 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 4 \times 225}{2 \times 4}

Simplify the expression

x = \frac{3 \pm ( - 3 ) ^{2} - 4 \times 4 \times 225}{8}

Simplify the expression

More Steps

x = \frac{3 \pm - 3591}{8}

Simplify the radical expression

More Steps

x = \frac{3 \pm 3 399 \times i}{8}

Separate the equation into 2 possible cases

x = \frac{3 + 3 399 \times i}{8} x = \frac{3 - 3 399 \times i}{8}

Simplify the expression

x = \frac{3}{8} + \frac{3 399}{8} i x = \frac{3 - 3 399 \times i}{8}

Simplify the expression

x = \frac{3}{8} + \frac{3 399}{8} i x = \frac{3}{8} - \frac{3 399}{8} i

Solution

x_{1} = \frac{3}{8} - \frac{3 399}{8} i, x_{2} = \frac{3}{8} + \frac{3 399}{8} i

Alternative Form

x_{1} \approx 0.375 - 7.490619 i, x_{2} \approx 0.375 + 7.490619 i

Factor the expression