j) \( 6 x^{2}+7 x=3 \) k) \( 3 x^{2}+5 x-2=0 \) l) \( 5 x^{2}+19 x-4=0 \)

To solve the quadratic equation \(6x^{2}+7x-3=0\), we can use the quadratic formula: \(x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\). Here, \(a=6\), \(b=7\), and \(c=-3\). Plugging in these values gives us \(x=\frac{-7\pm\sqrt{7^2-4(6)(-3)}}{2(6)}\). Simplifying further will lead you to find the roots. For the equation \(3x^{2}+5x-2=0\), find \(a=3\), \(b=5\), and \(c=-2\) and apply the quadratic formula. After the calculations, you'll get the values of \(x\) that satisfy this equation. Lastly, for \(5x^{2}+19x-4=0\), you again use \(a=5\), \(b=19\), and \(c=-4\) in the quadratic formula to derive the solutions. Always ensure to simplify under the square root for clear results!