Solve ((2x-7)/5)=(x^2)/3

Question

Solve the equation(The real numbers system)

x \in / R

Alternative Form

No real solution

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Solve using the quadratic formula in the complex numbers system

Solve using the PQ formula in the complex numbers system

x_{1} = \frac{3}{5} - \frac{4 6}{5} i, x_{2} = \frac{3}{5} + \frac{4 6}{5} i

Alternative Form

x_{1} \approx 0.6 - 1.959592 i, x_{2} \approx 0.6 + 1.959592 i

Evaluate

\frac{2 x - 7}{5} = \frac{x ^{2}}{3}

Swap the sides

\frac{x ^{2}}{3} = \frac{2 x - 7}{5}

Rewrite the expression

\frac{1}{3} x^{2} = \frac{2 x - 7}{5}

Rewrite the expression

\frac{1}{3} x^{2} = \frac{2}{5} x - \frac{7}{5}

Move the expression to the left side

\frac{1}{3} x^{2} - \frac{2}{5} x + \frac{7}{5} = 0

Multiply both sides

15 (\frac{1}{3} x^{2} - \frac{2}{5} x + \frac{7}{5}) = 15 \times 0

Calculate

5 x^{2} - 6 x + 21 = 0

Substitute a= 5,b= - 6 and c= 21 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 5 \times 21}{2 \times 5}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 5 \times 21}{10}

Simplify the expression

More Steps

x = \frac{6 \pm - 384}{10}

Simplify the radical expression

More Steps

x = \frac{6 \pm 8 6 \times i}{10}

Separate the equation into 2 possible cases

x = \frac{6 + 8 6 \times i}{10} x = \frac{6 - 8 6 \times i}{10}

Simplify the expression

More Steps

x = \frac{3}{5} + \frac{4 6}{5} i x = \frac{6 - 8 6 \times i}{10}

Simplify the expression

More Steps

x = \frac{3}{5} + \frac{4 6}{5} i x = \frac{3}{5} - \frac{4 6}{5} i

Solution

x_{1} = \frac{3}{5} - \frac{4 6}{5} i, x_{2} = \frac{3}{5} + \frac{4 6}{5} i

Alternative Form

x_{1} \approx 0.6 - 1.959592 i, x_{2} \approx 0.6 + 1.959592 i

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