Let's solve the quadratic equation X squared plus 5x minus 4 equals 15. First, we need to rewrite this equation in standard form by moving all terms to one side. We subtract 15 from both sides to get X squared plus 5x minus 19 equals 0.
Now we identify the coefficients from our standard form equation X squared plus 5x minus 19 equals 0. Comparing with the general form ax squared plus bx plus c equals 0, we can see that a equals 1, b equals 5, and c equals negative 19.
Now we apply the quadratic formula. The formula is X equals negative b plus or minus the square root of b squared minus 4ac, all divided by 2a. Substituting our values a equals 1, b equals 5, and c equals negative 19, we get X equals negative 5 plus or minus the square root of 5 squared minus 4 times 1 times negative 19, all divided by 2 times 1.
Now let's simplify the discriminant. We have 5 squared minus 4 times 1 times negative 19, which equals 25 minus negative 76, or 25 plus 76, which equals 101. Therefore, our final answer is X equals negative 5 plus or minus the square root of 101, all divided by 2. This gives us two solutions for the quadratic equation.
To summarize our solution: We solved the quadratic equation X squared plus 5x minus 4 equals 15. We rewrote it in standard form, identified the coefficients, applied the quadratic formula, and simplified to get our final answer: X equals negative 5 plus or minus the square root of 101, all divided by 2.