[tex]15x^2-10x-5=0\\ \\ a=15, \ \ b=-10 \ \ c=-5\\ \\ \Delta = b^{2}-4ac = (-10)^{2}-4* 15* (-5)= 100+300=400\\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a} =\frac{10- \sqrt{400}}{2*15}=\frac{10-20}{30}= \frac{-10}{30}=-\frac{1}{3}\\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a} =\frac{10+ \sqrt{400}}{2*15}=\frac{10+20}{30}= \frac{30}{30}=1 \\ \\ \ 15x^2-10x-5=15(x+ \frac{1}{3})(x-1)= (15x+ \frac{1}{3}*15)(x-1)=(15x+5)(x-1)\\ \\ Answer :15x^2-10x-5 =(15x+5)(x-1)[/tex]
