What are the solutions to the equation -1/3 q^2-10q+112= 1/4 q^2+5q+1 ?

The solutions to the equation -1/3 q^2-10q+112= 1/4 q^2+5q+1 are q=-222/7 ,q=6

Find the zeros of -1/3 q^2-10q+112= 1/4 q^2+5q+1

The zeros of -1/3 q^2-10q+112= 1/4 q^2+5q+1 are q=-222/7 ,q=6

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- \frac{1}{3} q^{2} - 10 q + 112 = \frac{1}{4} q^{2} + 5 q + 1

q = - \frac{222}{7}, q = 6

Decimal Notation

q = - 31.71428 \dots, q = 6

Solution steps

- \frac{1}{3} q^{2} - 10 q + 112 = \frac{1}{4} q^{2} + 5 q + 1

Find Least Common Multiplier of

3, 4 : 12

Multiply by LCM=

12

- \frac{1}{3} q^{2} \cdot 12 - 10 q \cdot 12 + 112 \cdot 12 = \frac{1}{4} q^{2} \cdot 12 + 5 q \cdot 12 + 1 \cdot 12

Simplify

- 4 q^{2} - 120 q + 1344 = 3 q^{2} + 60 q + 12

Move

12

to the left side

- 4 q^{2} - 120 q + 1332 = 3 q^{2} + 60 q

Move

60 q

to the left side

- 4 q^{2} - 180 q + 1332 = 3 q^{2}

Move

3 q^{2}

to the left side

- 7 q^{2} - 180 q + 1332 = 0

Solve with the quadratic formula

q_{1, 2} = \frac{- ( - 180 ) \pm ( - 180 ) ^{2} - 4 ( - 7 ) \cdot 1332}{2 ( - 7 )}

(- 180)^{2} - 4 (- 7) \cdot 1332 = 264

q_{1, 2} = \frac{- ( - 180 ) \pm 264}{2 ( - 7 )}

Separate the solutions

q_{1} = \frac{- ( - 180 ) + 264}{2 ( - 7 )}, q_{2} = \frac{- ( - 180 ) - 264}{2 ( - 7 )}

q = \frac{- ( - 180 ) + 264}{2 ( - 7 )} : - \frac{222}{7}

q = \frac{- ( - 180 ) - 264}{2 ( - 7 )} : 6

The solutions to the quadratic equation are:

q = - \frac{222}{7}, q = 6

7 x^{2} - 8 x - 6 = 0

2 x^{2} - 8 x + 8 = 0

468 = 500 - 2 x^{2}

250 (x) (\frac{x}{2}) = 8 (1473) (600 - x)

\frac{x ^{2}}{2} + \frac{10 x}{3} + 2 = 0

What are the solutions to the equation -1/3 q^2-10q+112= 1/4 q^2+5q+1 ?
The solutions to the equation -1/3 q^2-10q+112= 1/4 q^2+5q+1 are q=-222/7 ,q=6
Find the zeros of -1/3 q^2-10q+112= 1/4 q^2+5q+1
The zeros of -1/3 q^2-10q+112= 1/4 q^2+5q+1 are q=-222/7 ,q=6