Question

Solve by using the quadratic formula.
15x^2 - 1 = 2x

Answer 1

`15x^2 - 1 = 2x \\\\15x^2-2x - 1 = 0\\ \\a=15, \ \ b=-2 , \ \ c=-1 \\ \\\Delta =b^2-4ac = (-2)^2 -4\cdot 15 \cdot (-1) = 4+60=64 \\ \\x_(1)=(-b-√(\Delta) )/(2a)=(-(-2)-√(64))/(2\cdot 15 )=( 2-8)/(30)=(-6)/(30)=- (1)/(5)\\ \\x_(2)=(-b+√(\Delta) )/(2a)=(-(-2)+√(64))/(2\cdot 15 )=( 2+8)/(30)=(10)/(30)= (1)/(3)`

Answer 2

`15x^2-1=2x\\\\15x^2-2x-1=0\\\\a=15;\ b=-2;\ c=-1\\\\\Delta=b^2-4ac\to\Delta=(-2)^2-4\cdot15\cdot(-1)=4+60=64\\\\x_1=(-b-\sqrt\Delta)/(2)a;\ x_2=(-b+\sqrt\Delta)/(2a)\\\\\sqrt\Delta=√(64)=8\\\\x_1=(2-8)/(2\cdot15)=(-6)/(30)=-(1)/(5);\ x_2=(2+8)/(2\cdot15)=(10)/(30)=(1)/(3)`