What are the solutions to the equation 6x^2-84x+228=0 ?

The solutions to the equation 6x^2-84x+228=0 are x=7+sqrt(11),x=7-sqrt(11)

Find the zeros of 6x^2-84x+228=0

The zeros of 6x^2-84x+228=0 are x=7+sqrt(11),x=7-sqrt(11)

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6 x^{2} - 84 x + 228 = 0

x = 7 + 11, x = 7 - 11

Decimal Notation

x = 10.31662 \dots, x = 3.68337 \dots

Solution steps

6 x^{2} - 84 x + 228 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 84 ) \pm ( - 84 ) ^{2} - 4 \cdot 6 \cdot 228}{2 \cdot 6}

(- 84)^{2} - 4 \cdot 6 \cdot 228 = 1211

x_{1, 2} = \frac{- ( - 84 ) \pm 12 11}{2 \cdot 6}

Separate the solutions

x_{1} = \frac{- ( - 84 ) + 12 11}{2 \cdot 6}, x_{2} = \frac{- ( - 84 ) - 12 11}{2 \cdot 6}

x = \frac{- ( - 84 ) + 12 11}{2 \cdot 6} : 7 + 11

x = \frac{- ( - 84 ) - 12 11}{2 \cdot 6} : 7 - 11

The solutions to the quadratic equation are:

x = 7 + 11, x = 7 - 11

x^{2} - 6 x + 12

x^{2} + 6 x - 4

v^{2} = - 4

v^{2} = - 5

12 x^{2} - 13 x - 35 = 0

What are the solutions to the equation 6x^2-84x+228=0 ?
The solutions to the equation 6x^2-84x+228=0 are x=7+sqrt(11),x=7-sqrt(11)
Find the zeros of 6x^2-84x+228=0
The zeros of 6x^2-84x+228=0 are x=7+sqrt(11),x=7-sqrt(11)