To determine the number of real solutions for the quadratic equation \( 4x^2 + 3x - 7 = 0 \) using the discriminant, we first need to identify the coefficients \(a\), \(b\), and \(c\) from the equation in the standard form \( ax^2 + bx + c = 0 \):
- \( a = 4 \)
- \( b = 3 \)
- \( c = -7 \)
The discriminant \(D\) is calculated using the formula:
\[ D = b^2 - 4ac \]
Substituting in the values:
\[ D = 3^2 - 4(4)(-7) \]
\[ D = 9 - 4(4)(-7) \] \[ D = 9 - (-112) \] \[ D = 9 + 112 \] \[ D = 121 \]
Since the discriminant \(D\) is positive (\(121 > 0\)), this means that the quadratic equation has two distinct real solutions.
Therefore, the correct response is:
"There will be two real solutions since the discriminant is positive."