9) 2x^2-3x-15-5 10) x^2+2x-1=2 11) 2k^2+9k=-7 12) 5r^2=80

9) To solve the equation $2x^{2}-3x-15-5$, we first simplify the equation by combining like terms:<br /><br />$2x^{2}-3x-20=0$<br /><br />Next, we can factor the quadratic equation:<br /><br />$(2x+5)(x-4)=0$<br /><br />Setting each factor equal to zero gives us the solutions:<br /><br />$2x+5=0$ or $x-4=0$<br /><br />Solving for $x$, we get:<br /><br />$x=-\frac{5}{2}$ or $x=4$<br /><br />Therefore, the solutions to the equation $2x^{2}-3x-15-5$ are $x=-\frac{5}{2}$ and $x=4$.<br /><br />10) To solve the equation $x^{2}+2x-1=2$, we first move all terms to one side of the equation:<br /><br />$x^{2}+2x-3=0$<br /><br />Next, we can factor the quadratic equation:<br /><br />$(x+3)(x-1)=0$<br /><br />Setting each factor equal to zero gives us the solutions:<br /><br />$x+3=0$ or $x-1=0$<br /><br />Solving for $x$, we get:<br /><br />$x=-3$ or $x=1$<br /><br />Therefore, the solutions to the equation $x^{2}+2x-1=2$ are $x=-3$ and $x=1$.<br /><br />11) To solve the equation $2k^{2}+9k=-7$, we first move all terms to one side of the equation:<br /><br />$2k^{2}+9k+7=0$<br /><br />Next, we can use the quadratic formula to solve for $k$:<br /><br />$k=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$<br /><br />Plugging in the values $a=2$, $b=9$, and $c=7$, we get:<br /><br />$k=\frac{-9\pm\sqrt{9^{2}-4(2)(7)}}{2(2)}$<br /><br />$k=\frac{-9\pm\sqrt{81-56}}{4}$<br /><br />$k=\frac{-9\pm\sqrt{25}}{4}$<br /><br />$k=\frac{-9\pm5}{4}$<br /><br />Therefore, the solutions to the equation $2k^{2}+9k=-7$ are $k=\frac{-9+5}{4}=-1$ and $k=\frac{-9-5}{4}=-3.5$.<br /><br />12) To solve the equation $5r^{2}=80$, we first divide both sides by 5:<br /><br />$r^{2}=16$<br /><br />Next, we take the square root of both sides:<br /><br />$r=\pm4$<br /><br />Therefore, the solutions to the equation $5r^{2}=80$ are $r=4$ and $r=-4$.