Solve 4x^2-12x-15

Question

Find the roots

x_{1} = \frac{3 - 2 6}{2}, x_{2} = \frac{3 + 2 6}{2}

Alternative Form

x_{1} \approx - 0.94949, x_{2} \approx 3.94949

Evaluate

4 x^{2} - 12 x - 15

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

4 x^{2} - 12 x - 15 = 0

Substitute a= 4,b= - 12 and c= - 15 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 4 ( - 15 )}{2 \times 4}

Simplify the expression

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 4 ( - 15 )}{8}

Simplify the expression

More Steps

x = \frac{12 \pm 384}{8}

Simplify the radical expression

More Steps

x = \frac{12 \pm 8 6}{8}

Separate the equation into 2 possible cases

x = \frac{12 + 8 6}{8} x = \frac{12 - 8 6}{8}

Simplify the expression

More Steps

x = \frac{3 + 2 6}{2} x = \frac{12 - 8 6}{8}

Simplify the expression

More Steps

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

Solution

x_{1} = \frac{3 - 2 6}{2}, x_{2} = \frac{3 + 2 6}{2}

Alternative Form

x_{1} \approx - 0.94949, x_{2} \approx 3.94949

Show Solution