Solve any maths problem

Step by step

1. 0.6 v^{2} = 800

   Start from the equation as given.

2. 0.6 v^{2} - 800 = 0

   Bring everything to one side and collect like terms so the right-hand side is 0.

3. a = 0.6,\quad b = 0.0,\quad c = -800.0

   Read off the coefficients of the standard form ax² + bx + c = 0.

4. \Delta = b^2 - 4ac = (0.0)^2 - 4(0.6)(-800.0) = 1920.0

   It does not factor nicely, so use the discriminant Δ = b² − 4ac.

5. v = \frac{-b \pm \sqrt{\Delta}}{2a} = \frac{0.0 \pm \sqrt{1920.0}}{1.2}

   Δ > 0, so there are two distinct real roots. Substitute into the quadratic formula.

6. v = 36.51483717 \quad\text{or}\quad v = -36.51483717

   Simplify each root.