X^2+3x=4

To solve the equation \(x^2 + 3x = 4\), you can start by rearranging it into standard quadratic form:

\[ x^2 + 3x - 4 = 0 \]

Next, you can factor the quadratic, or you can use the quadratic formula. Let's try factoring first. We need two numbers that multiply to \(-4\) (the constant term) and add to \(3\) (the coefficient of \(x\)). The numbers \(4\) and \(-1\) fit this requirement:

\[ (x + 4)(x - 1) = 0 \]

Now, set each factor equal to zero:

1. \(x + 4 = 0 \quad \Rightarrow \quad x = -4\)
2. \(x - 1 = 0 \quad \Rightarrow \quad x = 1\)

Thus, the solutions to the equation \(x^2 + 3x = 4\) are:

\[ x = -4 \quad \text{and} \quad x = 1 \]