Solve 4x^2=16x-13

Evaluate

4 x^{2} = 16 x - 13

Move the expression to the left side

4 x^{2} - 16 x + 13 = 0

Substitute a= 4,b= - 16 and c= 13 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{16 \pm ( - 16 ) ^{2} - 4 \times 4 \times 13}{2 \times 4}

Simplify the expression

x = \frac{16 \pm ( - 16 ) ^{2} - 4 \times 4 \times 13}{8}

Simplify the expression

More Steps

x = \frac{16 \pm 48}{8}

Simplify the radical expression

More Steps

x = \frac{16 \pm 4 3}{8}

Separate the equation into 2 possible cases

x = \frac{16 + 4 3}{8} x = \frac{16 - 4 3}{8}

Simplify the expression

More Steps

x = \frac{4 + 3}{2} x = \frac{16 - 4 3}{8}

Simplify the expression

More Steps

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

Solution

x_{1} = \frac{4 - 3}{2}, x_{2} = \frac{4 + 3}{2}

Alternative Form

x_{1} \approx 1.133975, x_{2} \approx 2.866025

Solve the quadratic equation