Solve 13-3n = 2n^2 -8n

Evaluate

13 - 3 n = 2 n^{2} - 8 n

Swap the sides

2 n^{2} - 8 n = 13 - 3 n

Move the expression to the left side

2 n^{2} - 5 n - 13 = 0

Substitute a= 2,b= - 5 and c= - 13 into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{5 \pm ( - 5 ) ^{2} - 4 \times 2 ( - 13 )}{2 \times 2}

Simplify the expression

n = \frac{5 \pm ( - 5 ) ^{2} - 4 \times 2 ( - 13 )}{4}

Simplify the expression

More Steps

n = \frac{5 \pm 129}{4}

Separate the equation into 2 possible cases

n = \frac{5 + 129}{4} n = \frac{5 - 129}{4}

Solution

n_{1} = \frac{5 - 129}{4}, n_{2} = \frac{5 + 129}{4}

Alternative Form

n_{1} \approx - 1.589454, n_{2} \approx 4.089454

Solve the quadratic equation