Question

What are the solutions of the quadratic equation below 2x^2-2x-9=0

Answer 1

`2x^2-2x-9=0\\\\Use\ the\ quadratic\ formula\\\\ax^2+bx+c=0\\\\\Delta=b^2-4ac\\\\if\ \Delta > 0\ then\ solutions\ are\ equal\\\\x_1=(-b-\sqrt\Delta)/(2a)\ and\ x_2=(-b+\sqrt\Delta)/(2a)`

`a=2;\ b=-2;\ c=-9\\\\\Delta=(-2)^2-4\cdot2\cdpt(-9)=4+72=76 > 0\\\\\sqrt\Delta=√(76)=√(4\cdot19)=2√(19)\\\\x_1=(-(-2)-2√(19))/(2\cdot2)=(2-2√(19))/(4)=(1-√(19))/(2)\\\\x_2=(-(-2)+2√(19))/(2\cdot2)=(2+2√(19))/(4)=(1+√(19))/(2)`