Solve 4x^2 - 12x - 19

Question

Find the roots

x_{1} = \frac{3 - 2 7}{2}, x_{2} = \frac{3 + 2 7}{2}

Alternative Form

x_{1} \approx - 1.145751, x_{2} \approx 4.145751

Evaluate

4 x^{2} - 12 x - 19

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

4 x^{2} - 12 x - 19 = 0

Substitute a= 4,b= - 12 and c= - 19 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 4 ( - 19 )}{2 \times 4}

Simplify the expression

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 4 ( - 19 )}{8}

Simplify the expression

More Steps

x = \frac{12 \pm 448}{8}

Simplify the radical expression

More Steps

x = \frac{12 \pm 8 7}{8}

Separate the equation into 2 possible cases

x = \frac{12 + 8 7}{8} x = \frac{12 - 8 7}{8}

Simplify the expression

More Steps

x = \frac{3 + 2 7}{2} x = \frac{12 - 8 7}{8}

Simplify the expression

More Steps

x = \frac{3 + 2 7}{2} x = \frac{3 - 2 7}{2}

Solution

x_{1} = \frac{3 - 2 7}{2}, x_{2} = \frac{3 + 2 7}{2}

Alternative Form

x_{1} \approx - 1.145751, x_{2} \approx 4.145751

Show Solution