Solve the Quadratic: Unravel the Equation 5x² + 1.5x + 1 = 0

Solve the following equation:

$5x^2+1\frac{1}{2}x+1=0$

Let's solve the quadratic equation $5x^2 + 1.5x + 1 = 0$ using the quadratic formula.

Step 1: Identify the coefficients for the equation $ax^2 + bx + c = 0$:
$a = 5$
$b = 1.5$
$c = 1$

Step 2: Calculate the discriminant $\Delta = b^2 - 4ac$.
$\Delta = (1.5)^2 - 4 \cdot 5 \cdot 1 = 2.25 - 20 = -17.75$

Step 3: Analyze the discriminant:
Since the discriminant $\Delta = -17.75$ is negative, this indicates that there are no real solutions to the equation $5x^2 + 1.5x + 1 = 0$.

Therefore, the equation has no solution in the real number system.