Solve 3x-1/5x-3=2x 1/6x-5

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{21 - 591}{5}, x_{2} = \frac{21 + 591}{5}

Alternative Form

x_{1} \approx - 0.662098, x_{2} \approx 9.062098

Evaluate

3 x - \frac{1}{5} x - 3 = 2 x \times \frac{1}{6} x - 5

Subtract the terms

More Steps

\frac{14}{5} x - 3 = 2 x \times \frac{1}{6} x - 5

Multiply

More Steps

\frac{14}{5} x - 3 = \frac{1}{3} x^{2} - 5

Swap the sides

\frac{1}{3} x^{2} - 5 = \frac{14}{5} x - 3

Move the expression to the left side

\frac{1}{3} x^{2} - 2 - \frac{14}{5} x = 0

Rewrite in standard form

\frac{1}{3} x^{2} - \frac{14}{5} x - 2 = 0

Multiply both sides

15 (\frac{1}{3} x^{2} - \frac{14}{5} x - 2) = 15 \times 0

Calculate

5 x^{2} - 42 x - 30 = 0

Substitute a= 5,b= - 42 and c= - 30 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{42 \pm ( - 42 ) ^{2} - 4 \times 5 ( - 30 )}{2 \times 5}

Simplify the expression

x = \frac{42 \pm ( - 42 ) ^{2} - 4 \times 5 ( - 30 )}{10}

Simplify the expression

More Steps

x = \frac{42 \pm 2364}{10}

Simplify the radical expression

More Steps

x = \frac{42 \pm 2 591}{10}

Separate the equation into 2 possible cases

x = \frac{42 + 2 591}{10} x = \frac{42 - 2 591}{10}

Simplify the expression

More Steps

x = \frac{21 + 591}{5} x = \frac{42 - 2 591}{10}

Simplify the expression

More Steps

x = \frac{21 + 591}{5} x = \frac{21 - 591}{5}

Solution

x_{1} = \frac{21 - 591}{5}, x_{2} = \frac{21 + 591}{5}

Alternative Form

x_{1} \approx - 0.662098, x_{2} \approx 9.062098

Show Solution