Solve 4x^2 -20x= -13

Evaluate

4 x^{2} - 20 x = - 13

Move the expression to the left side

4 x^{2} - 20 x + 13 = 0

Substitute a= 4,b= - 20 and c= 13 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{20 \pm ( - 20 ) ^{2} - 4 \times 4 \times 13}{2 \times 4}

Simplify the expression

x = \frac{20 \pm ( - 20 ) ^{2} - 4 \times 4 \times 13}{8}

Simplify the expression

More Steps

x = \frac{20 \pm 192}{8}

Simplify the radical expression

More Steps

x = \frac{20 \pm 8 3}{8}

Separate the equation into 2 possible cases

x = \frac{20 + 8 3}{8} x = \frac{20 - 8 3}{8}

Simplify the expression

More Steps

x = \frac{5 + 2 3}{2} x = \frac{20 - 8 3}{8}

Simplify the expression

More Steps

x = \frac{5 + 2 3}{2} x = \frac{5 - 2 3}{2}

Solution

x_{1} = \frac{5 - 2 3}{2}, x_{2} = \frac{5 + 2 3}{2}

Alternative Form

x_{1} \approx 0.767949, x_{2} \approx 4.232051

Solve the quadratic equation