What are the solutions to the equation 3x^2-12x-45-24sqrt(3)=0 ?

The solutions to the equation 3x^2-12x-45-24sqrt(3)=0 are x=6+sqrt(3),x=-2-sqrt(3)

Find the zeros of 3x^2-12x-45-24sqrt(3)=0

The zeros of 3x^2-12x-45-24sqrt(3)=0 are x=6+sqrt(3),x=-2-sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

3 x^{2} - 12 x - 45 - 243 = 0

x = 6 + 3, x = - 2 - 3

Decimal Notation

x = 7.73205 \dots, x = - 3.73205 \dots

Solution steps

3 x^{2} - 12 x - 45 - 243 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 3 ( - 45 - 24 3 )}{2 \cdot 3}

(- 12)^{2} - 4 \cdot 3 (- 45 - 243) = 63 + 24

x_{1, 2} = \frac{- ( - 12 ) \pm ( 6 3 + 24 )}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 12 ) + 6 3 + 24}{2 \cdot 3}, x_{2} = \frac{- ( - 12 ) - ( 6 3 + 24 )}{2 \cdot 3}

x = \frac{- ( - 12 ) + 6 3 + 24}{2 \cdot 3} : 6 + 3

x = \frac{- ( - 12 ) - ( 6 3 + 24 )}{2 \cdot 3} : - 2 - 3

The solutions to the quadratic equation are:

x = 6 + 3, x = - 2 - 3

x^{2} - 8 x - 3

x^{2} - 8 x + 9

x^{2} - 8 x + 2

x^{2} - 10 x + 18 = 0

(x + 3) (x - 5) = 5

What are the solutions to the equation 3x^2-12x-45-24sqrt(3)=0 ?
The solutions to the equation 3x^2-12x-45-24sqrt(3)=0 are x=6+sqrt(3),x=-2-sqrt(3)
Find the zeros of 3x^2-12x-45-24sqrt(3)=0
The zeros of 3x^2-12x-45-24sqrt(3)=0 are x=6+sqrt(3),x=-2-sqrt(3)