Solve 4x^2-20x-15

Question

Find the roots

x_{1} = \frac{5 - 2 10}{2}, x_{2} = \frac{5 + 2 10}{2}

Alternative Form

x_{1} \approx - 0.662278, x_{2} \approx 5.662278

Evaluate

4 x^{2} - 20 x - 15

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

4 x^{2} - 20 x - 15 = 0

Substitute a= 4,b= - 20 and c= - 15 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{20 \pm ( - 20 ) ^{2} - 4 \times 4 ( - 15 )}{2 \times 4}

Simplify the expression

x = \frac{20 \pm ( - 20 ) ^{2} - 4 \times 4 ( - 15 )}{8}

Simplify the expression

More Steps

x = \frac{20 \pm 640}{8}

Simplify the radical expression

More Steps

x = \frac{20 \pm 8 10}{8}

Separate the equation into 2 possible cases

x = \frac{20 + 8 10}{8} x = \frac{20 - 8 10}{8}

Simplify the expression

More Steps

x = \frac{5 + 2 10}{2} x = \frac{20 - 8 10}{8}

Simplify the expression

More Steps

x = \frac{5 + 2 10}{2} x = \frac{5 - 2 10}{2}

Solution

x_{1} = \frac{5 - 2 10}{2}, x_{2} = \frac{5 + 2 10}{2}

Alternative Form

x_{1} \approx - 0.662278, x_{2} \approx 5.662278

Show Solution