What are the solutions to the equation (x(x+1))/2 =120 ?

The solutions to the equation (x(x+1))/2 =120 are x=15,x=-16

Find the zeros of (x(x+1))/2 =120

The zeros of (x(x+1))/2 =120 are x=15,x=-16

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\frac{x ( x + 1 )}{2} = 120

x = 15, x = - 16

Solution steps

\frac{x ( x + 1 )}{2} = 120

Multiply both sides by

2

x (x + 1) = 240

Expand

x (x + 1) : x^{2} + x

x^{2} + x = 240

Move

240

to the left side

x^{2} + x - 240 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- 1 \pm 1 ^{2} - 4 \cdot 1 \cdot ( - 240 )}{2 \cdot 1}

1^{2} - 4 \cdot 1 \cdot (- 240) = 31

x_{1, 2} = \frac{- 1 \pm 31}{2 \cdot 1}

Separate the solutions

x_{1} = \frac{- 1 + 31}{2 \cdot 1}, x_{2} = \frac{- 1 - 31}{2 \cdot 1}

x = \frac{- 1 + 31}{2 \cdot 1} : 15

x = \frac{- 1 - 31}{2 \cdot 1} : - 16

The solutions to the quadratic equation are:

x = 15, x = - 16

x^{2} - 37 x + 27 = 0

7 x^{2} - 66 x + 27 = 0

x^{2} + (x + 5)^{2} = 5 + 16 (3 - x)

x^{2} + 4 = 13

x, 4 x^{2} + 12 x + 3 = 0

What are the solutions to the equation (x(x+1))/2 =120 ?
The solutions to the equation (x(x+1))/2 =120 are x=15,x=-16
Find the zeros of (x(x+1))/2 =120
The zeros of (x(x+1))/2 =120 are x=15,x=-16