What are the solutions to the equation 4x^2-24x+33=0 ?

The solutions to the equation 4x^2-24x+33=0 are x=(6+sqrt(3))/2 ,x=(6-sqrt(3))/2

Find the zeros of 4x^2-24x+33=0

The zeros of 4x^2-24x+33=0 are x=(6+sqrt(3))/2 ,x=(6-sqrt(3))/2

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4 x^{2} - 24 x + 33 = 0

x = \frac{6 + 3}{2}, x = \frac{6 - 3}{2}

Decimal Notation

x = 3.86602 \dots, x = 2.13397 \dots

Solution steps

4 x^{2} - 24 x + 33 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 24 ) \pm ( - 24 ) ^{2} - 4 \cdot 4 \cdot 33}{2 \cdot 4}

(- 24)^{2} - 4 \cdot 4 \cdot 33 = 43

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

Separate the solutions

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

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

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

The solutions to the quadratic equation are:

x = \frac{6 + 3}{2}, x = \frac{6 - 3}{2}

x^{2} + 60 = - 16 x

0 = x^{2} + 6 x + 4

7 w - 3 (4 w + 8) = 11

8 x^{- 2}

\frac{3}{4} x - 2 x \leq 1 + 2

What are the solutions to the equation 4x^2-24x+33=0 ?
The solutions to the equation 4x^2-24x+33=0 are x=(6+sqrt(3))/2 ,x=(6-sqrt(3))/2
Find the zeros of 4x^2-24x+33=0
The zeros of 4x^2-24x+33=0 are x=(6+sqrt(3))/2 ,x=(6-sqrt(3))/2