Solve y^2+3/2\sqrt 5y-5

Evaluate

y^{2} + \frac{3}{2} 5 y - 5

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

y^{2} + \frac{3}{2} 5 y - 5 = 0

Find the domain

y^{2} + \frac{3}{2} 5 y - 5 = 0, y \geq 0

Calculate

y^{2} + \frac{3}{2} 5 y - 5 = 0

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

\frac{3}{2} 5 y = - y^{2} + 5

Rewrite the expression

5 y = \frac{2 ( - y ^{2} + 5 )}{3}

Evaluate

5 y = \frac{2 ( - y ^{2} + 5 )}{3}, \frac{2 ( - y ^{2} + 5 )}{3} \geq 0

Evaluate

More Steps

5 y = \frac{2 ( - y ^{2} + 5 )}{3}, - 5 \leq y \leq 5

Solve the equation for y

More Steps

y \approx 1.170793 y \approx 3.335527, - 5 \leq y \leq 5

Find the intersection

y \approx 1.170793

Check if the solution is in the defined range

y \approx 1.170793, y \geq 0

Solution

y \approx 1.170793

Factor the expression