Solve 10-9x^2+4x=-6x^2

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{2 - 34}{3}, x_{2} = \frac{2 + 34}{3}

Alternative Form

x_{1} \approx - 1.276984, x_{2} \approx 2.610317

Evaluate

10 - 9 x^{2} + 4 x = - 6 x^{2}

Move the expression to the left side

10 - 3 x^{2} + 4 x = 0

Rewrite in standard form

- 3 x^{2} + 4 x + 10 = 0

Multiply both sides

3 x^{2} - 4 x - 10 = 0

Substitute a= 3,b= - 4 and c= - 10 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 3 ( - 10 )}{2 \times 3}

Simplify the expression

x = \frac{4 \pm ( - 4 ) ^{2} - 4 \times 3 ( - 10 )}{6}

Simplify the expression

More Steps

x = \frac{4 \pm 136}{6}

Simplify the radical expression

More Steps

x = \frac{4 \pm 2 34}{6}

Separate the equation into 2 possible cases

x = \frac{4 + 2 34}{6} x = \frac{4 - 2 34}{6}

Simplify the expression

More Steps

x = \frac{2 + 34}{3} x = \frac{4 - 2 34}{6}

Simplify the expression

More Steps

x = \frac{2 + 34}{3} x = \frac{2 - 34}{3}

Solution

x_{1} = \frac{2 - 34}{3}, x_{2} = \frac{2 + 34}{3}

Alternative Form

x_{1} \approx - 1.276984, x_{2} \approx 2.610317

Show Solution