What are the solutions to the equation 3x^2-84x=-117 ?

The solutions to the equation 3x^2-84x=-117 are x=14+sqrt(157),x=14-sqrt(157)

Find the zeros of 3x^2-84x=-117

The zeros of 3x^2-84x=-117 are x=14+sqrt(157),x=14-sqrt(157)

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3 x^{2} - 84 x = - 117

x = 14 + 157, x = 14 - 157

Decimal Notation

x = 26.52996 \dots, x = 1.47003 \dots

Solution steps

3 x^{2} - 84 x = - 117

Move

117

to the left side

3 x^{2} - 84 x + 117 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 84 ) \pm ( - 84 ) ^{2} - 4 \cdot 3 \cdot 117}{2 \cdot 3}

(- 84)^{2} - 4 \cdot 3 \cdot 117 = 6157

x_{1, 2} = \frac{- ( - 84 ) \pm 6 157}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 84 ) + 6 157}{2 \cdot 3}, x_{2} = \frac{- ( - 84 ) - 6 157}{2 \cdot 3}

x = \frac{- ( - 84 ) + 6 157}{2 \cdot 3} : 14 + 157

x = \frac{- ( - 84 ) - 6 157}{2 \cdot 3} : 14 - 157

The solutions to the quadratic equation are:

x = 14 + 157, x = 14 - 157

f, f (x + 1) = 5 x^{2} + 3 x - 2

t, d = v t - \frac{1}{2} a t^{2}

40 x^{2} - 13 x + 1 = 0

25 (5 x - 3)^{2} + 6 = 22

0.7 t^{2} = 14 t

What are the solutions to the equation 3x^2-84x=-117 ?
The solutions to the equation 3x^2-84x=-117 are x=14+sqrt(157),x=14-sqrt(157)
Find the zeros of 3x^2-84x=-117
The zeros of 3x^2-84x=-117 are x=14+sqrt(157),x=14-sqrt(157)