2a^2-3a=20 solve for a
To solve the equation 2a^2 - 3a = 20 for a, we can follow these steps:
Step 1: Rearrange the equation. Move all terms to one side to set the equation equal to zero:
2a^2 - 3a - 20 = 0
Step 2: Factor the quadratic expression. In this case, the expression can be factored as follows:
(2a + 5)(a - 4) = 0
Step 3: Apply the zero product property. Set each factor equal to zero:
2a + 5 = 0 or a - 4 = 0
Step 4: Solve each equation separately:
For 2a + 5 = 0:
Subtract 5 from both sides:
2a = -5
Divide both sides by 2:
a = -5/2 or -2.5
For a - 4 = 0:
Add 4 to both sides:
a = 4
Therefore, the solutions to the equation 2a^2 - 3a = 20 are a = -2.5 and a = 4.