Question

how many real - number solutions does the equation have? $x^{2}+3x = 4$

Explanation:

Step1: Rewrite to standard quadratic form

$x^2 + 3x - 4 = 0$

Step2: Calculate discriminant $\Delta=b^2-4ac$

Here $a=1$, $b=3$, $c=-4$.
$\Delta = 3^2 - 4(1)(-4) = 9 + 16 = 25$

Step3: Analyze discriminant sign

Since $\Delta=25>0$, there are 2 distinct real solutions.

Answer:

2