What are the solutions to the equation 12x^2-180x+464=0 ?

The solutions to the equation 12x^2-180x+464=0 are x=(45+sqrt(633))/6 ,x=(45-sqrt(633))/6

Find the zeros of 12x^2-180x+464=0

The zeros of 12x^2-180x+464=0 are x=(45+sqrt(633))/6 ,x=(45-sqrt(633))/6

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12 x^{2} - 180 x + 464 = 0

x = \frac{45 + 633}{6}, x = \frac{45 - 633}{6}

Decimal Notation

x = 11.69324 \dots, x = 3.30675 \dots

Solution steps

12 x^{2} - 180 x + 464 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 180 ) \pm ( - 180 ) ^{2} - 4 \cdot 12 \cdot 464}{2 \cdot 12}

(- 180)^{2} - 4 \cdot 12 \cdot 464 = 4633

x_{1, 2} = \frac{- ( - 180 ) \pm 4 633}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 180 ) + 4 633}{2 \cdot 12}, x_{2} = \frac{- ( - 180 ) - 4 633}{2 \cdot 12}

x = \frac{- ( - 180 ) + 4 633}{2 \cdot 12} : \frac{45 + 633}{6}

x = \frac{- ( - 180 ) - 4 633}{2 \cdot 12} : \frac{45 - 633}{6}

The solutions to the quadratic equation are:

x = \frac{45 + 633}{6}, x = \frac{45 - 633}{6}

∣ 3 x - 1 ∣ = ∣ x + 5 ∣

∣ x + 1 ∣ = 2 x + 1

x (7 x - 5) = 12

6 x^{2} - 9 x + 2 = 0

4 (6 x - 10) = 8 x + 40

What are the solutions to the equation 12x^2-180x+464=0 ?
The solutions to the equation 12x^2-180x+464=0 are x=(45+sqrt(633))/6 ,x=(45-sqrt(633))/6
Find the zeros of 12x^2-180x+464=0
The zeros of 12x^2-180x+464=0 are x=(45+sqrt(633))/6 ,x=(45-sqrt(633))/6