What are the solutions to the equation 0=12x^2-72x+80 ?

The solutions to the equation 0=12x^2-72x+80 are x=(9+sqrt(21))/3 ,x=(9-sqrt(21))/3

Find the zeros of 0=12x^2-72x+80

The zeros of 0=12x^2-72x+80 are x=(9+sqrt(21))/3 ,x=(9-sqrt(21))/3

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0 = 12 x^{2} - 72 x + 80

x = \frac{9 + 21}{3}, x = \frac{9 - 21}{3}

Decimal Notation

x = 4.52752 \dots, x = 1.47247 \dots

Solution steps

0 = 12 x^{2} - 72 x + 80

Switch sides

12 x^{2} - 72 x + 80 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 72 ) \pm ( - 72 ) ^{2} - 4 \cdot 12 \cdot 80}{2 \cdot 12}

(- 72)^{2} - 4 \cdot 12 \cdot 80 = 821

x_{1, 2} = \frac{- ( - 72 ) \pm 8 21}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 72 ) + 8 21}{2 \cdot 12}, x_{2} = \frac{- ( - 72 ) - 8 21}{2 \cdot 12}

x = \frac{- ( - 72 ) + 8 21}{2 \cdot 12} : \frac{9 + 21}{3}

x = \frac{- ( - 72 ) - 8 21}{2 \cdot 12} : \frac{9 - 21}{3}

The solutions to the quadratic equation are:

x = \frac{9 + 21}{3}, x = \frac{9 - 21}{3}

y^{2} = 10 y - 16

2 y^{2} - 4 y

w^{2} + 4 w + 3 = 0

x^{2} + 2 x - 7

(x - 1)^{2} = 40

What are the solutions to the equation 0=12x^2-72x+80 ?
The solutions to the equation 0=12x^2-72x+80 are x=(9+sqrt(21))/3 ,x=(9-sqrt(21))/3
Find the zeros of 0=12x^2-72x+80
The zeros of 0=12x^2-72x+80 are x=(9+sqrt(21))/3 ,x=(9-sqrt(21))/3