8. 3x^2-5x=4-3x^2 9. 4x^2+9x=12x

8. To solve the equation $3x^{2}-5x=4-3x^{2}$, we first move all the terms to one side of the equation to set it equal to zero:<br /><br />$3x^{2}-5x-4+3x^{2}=0$<br /><br />Combining like terms, we get:<br /><br />$6x^{2}-5x-4=0$<br /><br />Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:<br /><br />$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$<br /><br />In this case, $a=6$, $b=-5$, and $c=-4$. Plugging these values into the quadratic formula, we get:<br /><br />$x=\frac{-(-5)\pm\sqrt{(-5)^{2}-4(6)(-4)}}{2(6)}$<br /><br />Simplifying further, we have:<br /><br />$x=\frac{5\pm\sqrt{25+96}}{12}$<br /><br />$x=\frac{5\pm\sqrt{121}}{12}$<br /><br />$x=\frac{5\pm11}{12}$<br /><br />So, the solutions to the equation are $x=\frac{16}{12}$ and $x=\frac{-6}{12}$, which simplify to $x=\frac{4}{3}$ and $x=-\frac{1}{2}$.<br /><br />9. To solve the equation $4x^{2}+9x=12x$, we first move all the terms to one side of the equation to set it equal to zero:<br /><br />$4x^{2}+9x-12x=0$<br /><br />Combining like terms, we get:<br /><br />$4x^{2}-3x=0$<br /><br />Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula:<br /><br />$x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$<br /><br />In this case, $a=4$, $b=-3$, and $c=0$. Plugging these values into the quadratic formula, we get:<br /><br />$x=\frac{-(-3)\pm\sqrt{(-3)^{2}-4(4)(0)}}{2(4)}$<br /><br />Simplifying further, we have:<br /><br />$x=\frac{3\pm\sqrt{9}}{8}$<br /><br />$x=\frac{3\pm3}{8}$<br /><br />So, the solutions to the equation are $x=\frac{6}{8}$ and $x=-\frac{0}{8}$, which simplify to $x=\frac{3}{4}$ and $x=0$.