Question

Use the quadratic formula to solve 7x2 – 4x - 5 = 0. x = 2 + √39 or x = 2 - √39
7 7
x = 4 + √39 or x = 4 - √39
7 7

x = 4 + √39 or x = 4 - √39
14 14
x = 2 + √39 or x = 2 - √39
14 14

Answer 1

Quadratic formula says that if you have a polynomial of the form \(ax^2+bx+c=0, a\ne 0\) the solutions can be found from \[x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\]Note that \(\pm\) is a shorthand for both the positive and negative signs, so you are really finding both
\[x=\frac{-b+\sqrt{b^2-4ac}}{2a}\]and
\[x=\frac{-b-\sqrt{b^2-4ac}}{2a}\]

In your equation, you have \(a=7, b=-4, c=-5\) so plug those into the formula and chug away.