Si \( x^{2}+x=12 \Rightarrow 2 x^{2}+x+2= \)

To solve the problem, we need to first find the value of \( x \) from the given equation \( x^{2} + x = 12 \). Then we can substitute this value into the second equation \( 2x^{2} + x + 2 \) to find the result. Let's start by solving the first equation: \[ x^{2} + x = 12 \] To solve this quadratic equation, we can rearrange it to the standard form: \[ x^{2} + x - 12 = 0 \] Now we can factor the quadratic equation: \[ (x + 4)(x - 3) = 0 \] Setting each factor equal to zero gives us the solutions for \( x \): \[ x + 4 = 0 \quad \text{or} \quad x - 3 = 0 \] \[ x = -4 \quad \text{or} \quad x = 3 \] Now we have two possible values for \( x \). We need to substitute each of these values into the second equation \( 2x^{2} + x + 2 \) to find the corresponding results. For \( x = -4 \): \[ 2(-4)^{2} + (-4) + 2 = 2(16) - 4 + 2 = 32 - 4 + 2 = 30 \] For \( x = 3 \): \[ 2(3)^{2} + 3 + 2 = 2(9) + 3 + 2 = 18 + 3 + 2 = 23 \] So, the two possible results for \( 2x^{2} + x + 2 \) are 30 and 23, depending on the value of \( x \).