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6x^2 - 2x = 7

6x^2 - 2x - 7 = 0

[tex] x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a} [/tex]

[tex] x = \dfrac{-(-2) \pm \sqrt{(-2)^2 - 4(6)(-7)}}{2(6)} [/tex]

[tex] x = \dfrac{2 \pm \sqrt{4 + 168}}{12} [/tex]

[tex] x = \dfrac{2 \pm \sqrt{172}}{12} [/tex]

[tex] x = \dfrac{2 \pm 2\sqrt{43}}{12} [/tex]

[tex] x = \dfrac{1 \pm \sqrt{43}}{6} [/tex]

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penfila11Pen penfila11Pen · Answer 2 · 2018-04-17T19:35:38+02:00

Hey there :)

6x² - 2x = 7

Bring all terms to one side and equate to 0
6x² - 2x - 7 = 0

Lets see if we can solve by factoring:
Sum = - 2 and Product = - 7
We do not have factors for this

Therefore, we need to solve by quadratic equation { Refer to the attached picture }

6x² - 2x - 7 = 0
↓ ↓ ↓
a b c

x = [tex] \frac{-(-2)+/- \sqrt{(-2)^2-4(6)(-7)} }{2(6)} [/tex]
x = [tex] \frac{2+/- \sqrt{ 172 } }{12} = \frac{2+/-2 \sqrt{43} }{12} [/tex]

x = [tex] \frac{1+/-\sqrt{43}}{6} [/tex]
↓
Will be your answer