## which equation shows the quadratic formula used correctly to solve 7×2 = 9 + x for x?

Equation \( 7x^2 = 9+x \)

=> \( 7x^2 -x -9 =0 \) [Convert in Quadaratic Equation]

=> \( 7x^2 + (-1)x + (-9) =0 \)

The Quadratic Equation formula is

\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}.\)

where a = 7, b = -1 and c = -9

put the Value of a, b, and c in the quadratic equation formula

=> \(x = {-(-1) \pm \sqrt{(-)^2-4(7)(-9)} \over 2(7)}\)

=> \(x = {1 \pm \sqrt{1-4(-63)} \over 14}\)

=> \(x = {1 \pm \sqrt{1+ 252} \over 14}\)

=> \(x = {1 \pm \sqrt{253} \over 14}\)

=> \(x = {1 \pm 15.9 \over 14}\)

=> \(x = {16.9 \over 14} \;and\; { -14.9 \over 14}\) [convert in Decimal Form]

=> \(x = {1.2} \;and\; {-1.06}\)