# How do you solve 5v^2-7v=1 using the quadratic formula?

May 15, 2017

Move everything so all terms are on one side of the = sign, and solve for zero using the Quadratic Formula. There are two answers: v=$\frac{7 \setminus \pm \sqrt{69}}{10}$.
Subtract 1 from both sides so you have $5 {v}^{2} - 7 v - 1 = 0$. The "standard form" of a quadratic is $a {x}^{2} + b x + c$, so first we have to identify a, b, and c in your equation: a=5, b= -7, and c= -1.
The quadratic formula is $\frac{- b \setminus \pm \sqrt{{b}^{2} - 4 a c}}{2 a}$. Plugging in your values, we get $\frac{- 7 \setminus \pm \sqrt{69}}{2 \cdot 5}$, or $v = \frac{7 \setminus \pm \sqrt{69}}{10}$. It looks a little funny, but you can't simplify it any more. You can check the answer by graphing the function on your calculator and asking for the function value at these points.
After graphing, hit 2nd, "Calc", "Value" on your TI, and type in either $\frac{7 + \sqrt{69}}{10}$ or $\frac{7 - \sqrt{69}}{10}$, and you'll get that $y = 0$.