13. \( 2 x^{2}+8 x-60=4 \)

Let's first simplify the equation by moving all terms to one side. Here’s how it looks after rearranging: \[ 2x^2 + 8x - 60 - 4 = 0 \] This simplifies to: \[ 2x^2 + 8x - 64 = 0 \] Now, we can divide through by 2 to make it easier: \[ x^2 + 4x - 32 = 0 \] Next, we can use the quadratic formula \( x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \). Here, \( a = 1 \), \( b = 4 \), and \( c = -32 \). So, let’s find the discriminant: \[ b^2 - 4ac = 4^2 - 4(1)(-32) = 16 + 128 = 144 \] Now substituting values into the quadratic formula: \[ x = \frac{{-4 \pm \sqrt{144}}}{2(1)} = \frac{{-4 \pm 12}}{2} \] This gives us two potential solutions: 1. \( x = \frac{{8}}{2} = 4 \) 2. \( x = \frac{{-16}}{2} = -8 \) So, the final solutions are \( x = 4 \) and \( x = -8 \). Now, you’ve got the answers—feel free to reach out if you need more on this topic!