Question

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

Answer 1

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

Answer 2

$15x^2 - 1 = 2x \\\\15x^2-2x - 1 = 0\\ \\a=15, \ \ b=-2 , \ \ c=-1 \\ \\\Delta =b^2-4ac = (-2)^2 -4\cdot 15 \cdot (-1) = 4+60=64 \\ \\x_{1}=\frac{-b-\sqrt{\Delta} }{2a}=\frac{-(-2)-\sqrt{64}}{2\cdot 15 }=\frac{ 2-8}{30}=\frac{-6}{30}=- \frac{1}{5}\\ \\x_{2}=\frac{-b+\sqrt{\Delta} }{2a}=\frac{-(-2)+\sqrt{64}}{2\cdot 15 }=\frac{ 2+8}{30}=\frac{10}{30}= \frac{1}{3}$