Solve x \sqrt 3x^2-2\sqrt 2x-2\sqrt 3=0

Question

Solve the equation

x \approx 1.522509

Evaluate

x (3 x)^{2} - 2 2 x - 23 = 0

Find the domain

More Steps

x (3 x)^{2} - 2 2 x - 23 = 0, x \geq 0

Multiply the terms

More Steps

3 x^{2} - 2 2 x - 23 = 0

Move the expression to the right-hand side and change its sign

- 2 2 x = - 3 x^{2} + 23

Rewrite the expression

2 x = \frac{3 x ^{2} - 2 3}{2}

Evaluate

2 x = \frac{3 x ^{2} - 2 3}{2}, \frac{3 x ^{2} - 2 3}{2} \geq 0

Evaluate

More Steps

2 x = \frac{3 x ^{2} - 2 3}{2}, x \in (- \infty, - \frac{4 108}{3}] \cup [\frac{4 108}{3}, + \infty)

Solve the equation for x

More Steps

x \approx 0.635097 x \approx 1.522509, x \in (- \infty, - \frac{4 108}{3}] \cup [\frac{4 108}{3}, + \infty)

Find the intersection

x \approx 1.522509

Check if the solution is in the defined range

x \approx 1.522509, x \geq 0

Find the intersection of the solution and the defined range

x \approx 1.522509

Solution

x \approx 1.522509

Show Solution