To solve the equation \(-15x^2 - 3 = 2(7x^2 - 1.5)\), we first simplify the right side:
\[ 2(7x^2 - 1.5) = 14x^2 - 3 \]
Now, rewrite the equation:
\[ -15x^2 - 3 = 14x^2 - 3 \]
Next, we can add \(3\) to both sides to eliminate the constants:
\[ -15x^2 = 14x^2 \]
Now, let's move all the terms involving \(x^2\) to one side:
\[ -15x^2 - 14x^2 = 0 \]
This simplifies to:
\[ -29x^2 = 0 \]
Now, divide both sides by \(-29\):
\[ x^2 = 0 \]
Taking the square root of both sides yields:
\[ x = 0 \]
Since this is the only solution, we have 1 real solution to the equation.
Thus, the number of real solutions is 1.
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