Solve 3x(x-1)=5x+2

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{4 - 22}{3}, x_{2} = \frac{4 + 22}{3}

Alternative Form

x_{1} \approx - 0.230139, x_{2} \approx 2.896805

Evaluate

3 x (x - 1) = 5 x + 2

Expand the expression

More Steps

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

Move the expression to the left side

3 x^{2} - 8 x - 2 = 0

Substitute a= 3,b= - 8 and c= - 2 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 3 ( - 2 )}{2 \times 3}

Simplify the expression

x = \frac{8 \pm ( - 8 ) ^{2} - 4 \times 3 ( - 2 )}{6}

Simplify the expression

More Steps

x = \frac{8 \pm 88}{6}

Simplify the radical expression

More Steps

x = \frac{8 \pm 2 22}{6}

Separate the equation into 2 possible cases

x = \frac{8 + 2 22}{6} x = \frac{8 - 2 22}{6}

Simplify the expression

More Steps

x = \frac{4 + 22}{3} x = \frac{8 - 2 22}{6}

Simplify the expression

More Steps

x = \frac{4 + 22}{3} x = \frac{4 - 22}{3}

Solution

x_{1} = \frac{4 - 22}{3}, x_{2} = \frac{4 + 22}{3}

Alternative Form

x_{1} \approx - 0.230139, x_{2} \approx 2.896805

Show Solution