Solve 9x^2 - 12x - 4

Question

Find the roots

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

Alternative Form

x_{1} \approx - 0.276142, x_{2} \approx 1.609476

Evaluate

9 x^{2} - 12 x - 4

To find the roots of the expression,set the expression equal to 0

9 x^{2} - 12 x - 4 = 0

Substitute a= 9,b= - 12 and c= - 4 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 9 ( - 4 )}{2 \times 9}

Simplify the expression

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 9 ( - 4 )}{18}

Simplify the expression

More Steps

x = \frac{12 \pm 288}{18}

Simplify the radical expression

More Steps

x = \frac{12 \pm 12 2}{18}

Separate the equation into 2 possible cases

x = \frac{12 + 12 2}{18} x = \frac{12 - 12 2}{18}

Simplify the expression

More Steps

x = \frac{2 + 2 2}{3} x = \frac{12 - 12 2}{18}

Simplify the expression

More Steps

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

Solution

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

Alternative Form

x_{1} \approx - 0.276142, x_{2} \approx 1.609476

Show Solution