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

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

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

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

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

q = 7 + 11, q = 7 - 11

Decimal Notation

q = 10.31662 \dots, q = 3.68337 \dots

Solution steps

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

Solve with the quadratic formula

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

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

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

q = 7 + 11, q = 7 - 11

y^{2} - 24 y + 144 = 0

x, x^{2} - 7 x + 10 = 0

12 x^{2} - 48 x + 32 = 0

2 w^{2} + 7 w - 3 = 0

20 x^{2} - 9 x + 1 = 0

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