To find the solution of the equation \( \frac{7}{4} x^{2}-2=-0.5 x+4 \), we first rewrite it in standard form as \( \frac{7}{4} x^{2} + 0.5 x - 6 = 0 \). We then apply the quadratic formula, which is given by \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). Here, we identify \( a = \frac{7}{4} \), \( b = 0.5 \), and \( c = -6 \). After substituting these values into the formula and simplifying, we find two potential solutions for \( x \): \( x_1 = \frac{6}{7} \) and \( x_2 = -7 \). Therefore, one of the solutions to the equation is \( x = -7 \).