What are the solutions to the equation 3x^2-24x+27=0 ?

The solutions to the equation 3x^2-24x+27=0 are x=4+sqrt(7),x=4-sqrt(7)

Find the zeros of 3x^2-24x+27=0

The zeros of 3x^2-24x+27=0 are x=4+sqrt(7),x=4-sqrt(7)

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3 x^{2} - 24 x + 27 = 0

x = 4 + 7, x = 4 - 7

Decimal Notation

x = 6.64575 \dots, x = 1.35424 \dots

Solution steps

3 x^{2} - 24 x + 27 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 \cdot 3 \cdot 27}{2 \cdot 3}

(- 24)^{2} - 4 \cdot 3 \cdot 27 = 67

x_{1, 2} = \frac{- ( - 24 ) \pm 6 7}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 24 ) + 6 7}{2 \cdot 3}, x_{2} = \frac{- ( - 24 ) - 6 7}{2 \cdot 3}

x = \frac{- ( - 24 ) + 6 7}{2 \cdot 3} : 4 + 7

x = \frac{- ( - 24 ) - 6 7}{2 \cdot 3} : 4 - 7

The solutions to the quadratic equation are:

x = 4 + 7, x = 4 - 7

3 = (1 - 2 (1) + 5) t^{2} + (2 (1) - 2 (1)) t + 1

x^{2} + 4^{2} = 7^{2}

2 y^{2} + 16 y = - 8

(x - 4)^{2} + (x - 7)^{2} = 15

y, y^{2} (2 - x) = x^{3}

What are the solutions to the equation 3x^2-24x+27=0 ?
The solutions to the equation 3x^2-24x+27=0 are x=4+sqrt(7),x=4-sqrt(7)
Find the zeros of 3x^2-24x+27=0
The zeros of 3x^2-24x+27=0 are x=4+sqrt(7),x=4-sqrt(7)