Solve 5x 1/9x -15 - 7/3x-5 = 10/3x-5

Evaluate

5 x \times \frac{1}{9} x - 15 - \frac{7}{3} x - 5 = \frac{10}{3} x - 5

Simplify

More Steps

\frac{5}{9} x^{2} - 20 - \frac{7}{3} x = \frac{10}{3} x - 5

Move the expression to the left side

\frac{5}{9} x^{2} - 15 - \frac{17}{3} x = 0

Rewrite in standard form

\frac{5}{9} x^{2} - \frac{17}{3} x - 15 = 0

Multiply both sides

9 (\frac{5}{9} x^{2} - \frac{17}{3} x - 15) = 9 \times 0

Calculate

5 x^{2} - 51 x - 135 = 0

Substitute a= 5,b= - 51 and c= - 135 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{51 \pm ( - 51 ) ^{2} - 4 \times 5 ( - 135 )}{2 \times 5}

Simplify the expression

x = \frac{51 \pm ( - 51 ) ^{2} - 4 \times 5 ( - 135 )}{10}

Simplify the expression

More Steps

x = \frac{51 \pm 5301}{10}

Simplify the radical expression

More Steps

x = \frac{51 \pm 3 589}{10}

Separate the equation into 2 possible cases

x = \frac{51 + 3 589}{10} x = \frac{51 - 3 589}{10}

Solution

x_{1} = \frac{51 - 3 589}{10}, x_{2} = \frac{51 + 3 589}{10}

Alternative Form

x_{1} \approx - 2.180797, x_{2} \approx 12.380797

Solve the quadratic equation