Answers:
[tex]\begin{gathered} y=\frac{7-\sqrt[]{21}}{14} \\ or \\ y=\frac{7+\sqrt[]{21}}{14} \end{gathered}[/tex]
Explanation:
To use the quadratic formula, the equation should have the following form:
[tex]ax^2+bx+c=0[/tex]
So, a is the number beside the y^2, b is the number beside y and c is the constant value.
Then, subtracting 1 from both sides of the equation, we get:
[tex]\begin{gathered} -7y^2+7y=1 \\ -7y^2+7y-1=1-1 \\ -7y^2+7y-1=0 \end{gathered}[/tex]
Therefore, the value of a is -7, the value of b is 7 and the value of c is -1. So, the discriminant is equal to:
[tex]\begin{gathered} b^2-4ac=7^2-4(-7)(-1) \\ b^2-4ac=49-28 \\ b^2-4ac=21 \end{gathered}[/tex]
Since the value of the discriminant is positive, we have two different real solutions. So, we can solve the quadratic equation as follows:
[tex]\begin{gathered} y=\frac{-b\pm\sqrt[]{b^2-4ac}}{2a} \\ y=\frac{-7_{}\pm\sqrt[]{21}}{2(-7)}=\frac{-7\pm\sqrt[]{21}}{-14} \end{gathered}[/tex]
Therefore, the solutions of the equation are:
[tex]\begin{gathered} y=\frac{-7+\sqrt[]{21}}{-14}=\frac{7-\sqrt[]{21}}{14} \\ or \\ y=\frac{-7-\sqrt[]{21}}{-14}=\frac{7+\sqrt[]{21}}{14} \end{gathered}[/tex]
