What are the solutions to the equation 12x^2-112x+180=0 ?

The solutions to the equation 12x^2-112x+180=0 are x=(14+sqrt(61))/3 ,x=(14-sqrt(61))/3

Find the zeros of 12x^2-112x+180=0

The zeros of 12x^2-112x+180=0 are x=(14+sqrt(61))/3 ,x=(14-sqrt(61))/3

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12 x^{2} - 112 x + 180 = 0

x = \frac{14 + 61}{3}, x = \frac{14 - 61}{3}

Decimal Notation

x = 7.27008 \dots, x = 2.06325 \dots

Solution steps

12 x^{2} - 112 x + 180 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 112 ) \pm ( - 112 ) ^{2} - 4 \cdot 12 \cdot 180}{2 \cdot 12}

(- 112)^{2} - 4 \cdot 12 \cdot 180 = 861

x_{1, 2} = \frac{- ( - 112 ) \pm 8 61}{2 \cdot 12}

Separate the solutions

x_{1} = \frac{- ( - 112 ) + 8 61}{2 \cdot 12}, x_{2} = \frac{- ( - 112 ) - 8 61}{2 \cdot 12}

x = \frac{- ( - 112 ) + 8 61}{2 \cdot 12} : \frac{14 + 61}{3}

x = \frac{- ( - 112 ) - 8 61}{2 \cdot 12} : \frac{14 - 61}{3}

The solutions to the quadratic equation are:

x = \frac{14 + 61}{3}, x = \frac{14 - 61}{3}

\frac{x ^{2}}{8} = \frac{1}{2}

x^{2} + 15 x - 2 = 0

(x + 8)^{2} = 4

7 x^{2} + 17 x + 6 = 0

3 y^{2} - 27 = 0

What are the solutions to the equation 12x^2-112x+180=0 ?
The solutions to the equation 12x^2-112x+180=0 are x=(14+sqrt(61))/3 ,x=(14-sqrt(61))/3
Find the zeros of 12x^2-112x+180=0
The zeros of 12x^2-112x+180=0 are x=(14+sqrt(61))/3 ,x=(14-sqrt(61))/3