[tex]5x^2-6x-5=0\\\\a=5, \ b=-6, \ c=-5\\\\\Delta=b^2-4ac\rightarrow(-6)^2-4\cdot5\cdot(-5)=36+100=136\\\\\sqrt{\Delta}=\sqrt{136}=\sqrt{4\cdot34}=2\sqrt{34}\\\\x_1=\frac{-b-\sqrt{\Delta}}{2a}\rightarrow\frac{-(-6)-2\sqrt{34}}{2\cdot5}=\frac{6-2\sqrt{34}}{10}=\frac{3-\sqrt{34}}{5}\\\\x_2=\frac{-b+\sqrt{\Delta}}{2a}\rightarrow\frac{-(-6)+2\sqrt{34}}{2\cdot5}=\frac{6+2\sqrt{34}}{10}=\frac{3+\sqrt{34}}{5}[/tex]
