What are the solutions to the equation 5x-10=3x^2 ?

The solutions to the equation 5x-10=3x^2 are x= 5/6+i(sqrt(95))/6 ,x= 5/6-i(sqrt(95))/6

Find the zeros of 5x-10=3x^2

The zeros of 5x-10=3x^2 are x= 5/6+i(sqrt(95))/6 ,x= 5/6-i(sqrt(95))/6

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5 x - 10 = 3 x^{2}

x = \frac{5}{6} + i \frac{95}{6}, x = \frac{5}{6} - i \frac{95}{6}

Solution steps

5 x - 10 = 3 x^{2}

Switch sides

3 x^{2} = 5 x - 10

Move

10

to the left side

3 x^{2} + 10 = 5 x

Move

5 x

to the left side

3 x^{2} + 10 - 5 x = 0

Write in the standard form

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

3 x^{2} - 5 x + 10 = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - 5 ) \pm ( - 5 ) ^{2} - 4 \cdot 3 \cdot 10}{2 \cdot 3}

Simplify

(- 5)^{2} - 4 \cdot 3 \cdot 10 : 95 i

x_{1, 2} = \frac{- ( - 5 ) \pm 95 i}{2 \cdot 3}

Separate the solutions

x_{1} = \frac{- ( - 5 ) + 95 i}{2 \cdot 3}, x_{2} = \frac{- ( - 5 ) - 95 i}{2 \cdot 3}

x = \frac{- ( - 5 ) + 95 i}{2 \cdot 3} : \frac{5}{6} + i \frac{95}{6}

x = \frac{- ( - 5 ) - 95 i}{2 \cdot 3} : \frac{5}{6} - i \frac{95}{6}

The solutions to the quadratic equation are:

x = \frac{5}{6} + i \frac{95}{6}, x = \frac{5}{6} - i \frac{95}{6}

(8 \cdot 320)^{\frac{1}{3}}

\frac{- 5}{4 ^{2}}

5 x^{2} + 46 x - 40

\frac{2}{3} 4^{\frac{3}{2}}

3 x^{2} - 6 = - 54

What are the solutions to the equation 5x-10=3x^2 ?
The solutions to the equation 5x-10=3x^2 are x= 5/6+i(sqrt(95))/6 ,x= 5/6-i(sqrt(95))/6
Find the zeros of 5x-10=3x^2
The zeros of 5x-10=3x^2 are x= 5/6+i(sqrt(95))/6 ,x= 5/6-i(sqrt(95))/6