What are the solutions to the equation 3t^2=12t-15 ?

The solutions to the equation 3t^2=12t-15 are t=2+i,t=2-i

Find the zeros of 3t^2=12t-15

The zeros of 3t^2=12t-15 are t=2+i,t=2-i

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3 t^{2} = 12 t - 15

t = 2 + i, t = 2 - i

Solution steps

3 t^{2} = 12 t - 15

Move

15

to the left side

3 t^{2} + 15 = 12 t

Move

12 t

to the left side

3 t^{2} + 15 - 12 t = 0

Write in the standard form

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

3 t^{2} - 12 t + 15 = 0

Solve with the quadratic formula

t_{1, 2} = \frac{- ( - 12 ) \pm ( - 12 ) ^{2} - 4 \cdot 3 \cdot 15}{2 \cdot 3}

Simplify

(- 12)^{2} - 4 \cdot 3 \cdot 15 : 6 i

t_{1, 2} = \frac{- ( - 12 ) \pm 6 i}{2 \cdot 3}

Separate the solutions

t_{1} = \frac{- ( - 12 ) + 6 i}{2 \cdot 3}, t_{2} = \frac{- ( - 12 ) - 6 i}{2 \cdot 3}

t = \frac{- ( - 12 ) + 6 i}{2 \cdot 3} : 2 + i

t = \frac{- ( - 12 ) - 6 i}{2 \cdot 3} : 2 - i

The solutions to the quadratic equation are:

t = 2 + i, t = 2 - i

x^{2} - 3 x - 2 = 0

x^{2} + 4 x + 11

- 2 x^{2} - 3 x - 5 = 0

5 x^{2} = 12 x + 8

x (2 - x) = 5 (x - 2)

What are the solutions to the equation 3t^2=12t-15 ?
The solutions to the equation 3t^2=12t-15 are t=2+i,t=2-i
Find the zeros of 3t^2=12t-15
The zeros of 3t^2=12t-15 are t=2+i,t=2-i