What are the solutions to the equation 3/2 t^2=5t+5/7 t^2 ?

The solutions to the equation 3/2 t^2=5t+5/7 t^2 are t=0,t= 70/11

Find the zeros of 3/2 t^2=5t+5/7 t^2

The zeros of 3/2 t^2=5t+5/7 t^2 are t=0,t= 70/11

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\frac{3}{2} t^{2} = 5 t + \frac{5}{7} t^{2}

t = 0, t = \frac{70}{11}

Decimal Notation

t = 0, t = 6.36363 \dots

Solution steps

\frac{3}{2} t^{2} = 5 t + \frac{5}{7} t^{2}

Find Least Common Multiplier of

2, 7 : 14

Multiply by LCM=

14

\frac{3}{2} t^{2} \cdot 14 = 5 t \cdot 14 + \frac{5}{7} t^{2} \cdot 14

Simplify

21 t^{2} = 70 t + 10 t^{2}

Switch sides

70 t + 10 t^{2} = 21 t^{2}

Move

21 t^{2}

to the left side

70 t - 11 t^{2} = 0

Write in the standard form

a x^{2} + b x + c = 0

- 11 t^{2} + 70 t = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- 70 \pm 7 0 ^{2} - 4 ( - 11 ) \cdot 0}{2 ( - 11 )}

7 0^{2} - 4 (- 11) \cdot 0 = 70

t_{1, 2} = \frac{- 70 \pm 70}{2 ( - 11 )}

Separate the solutions

t_{1} = \frac{- 70 + 70}{2 ( - 11 )}, t_{2} = \frac{- 70 - 70}{2 ( - 11 )}

t = \frac{- 70 + 70}{2 ( - 11 )} : 0

t = \frac{- 70 - 70}{2 ( - 11 )} : \frac{70}{11}

The solutions to the quadratic equation are:

t = 0, t = \frac{70}{11}

∣ 2 - 3 x ∣ \leq 6

z^{2} + 4 z - 12 = 0

203

2 x^{2} = 19 x + 33

- \frac{4}{7} x = - 1

What are the solutions to the equation 3/2 t^2=5t+5/7 t^2 ?
The solutions to the equation 3/2 t^2=5t+5/7 t^2 are t=0,t= 70/11
Find the zeros of 3/2 t^2=5t+5/7 t^2
The zeros of 3/2 t^2=5t+5/7 t^2 are t=0,t= 70/11