Solve 5(n^2)-8=2n

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

n_{1} = \frac{1 - 41}{5}, n_{2} = \frac{1 + 41}{5}

Alternative Form

n_{1} \approx - 1.080625, n_{2} \approx 1.480625

Evaluate

5 n^{2} - 8 = 2 n

Move the expression to the left side

5 n^{2} - 8 - 2 n = 0

Rewrite in standard form

5 n^{2} - 2 n - 8 = 0

Substitute a= 5,b= - 2 and c= - 8 into the quadratic formula n = \frac{- b \pm b ^{2} - 4 a c}{2 a}

n = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 5 ( - 8 )}{2 \times 5}

Simplify the expression

n = \frac{2 \pm ( - 2 ) ^{2} - 4 \times 5 ( - 8 )}{10}

Simplify the expression

More Steps

n = \frac{2 \pm 164}{10}

Simplify the radical expression

More Steps

n = \frac{2 \pm 2 41}{10}

Separate the equation into 2 possible cases

n = \frac{2 + 2 41}{10} n = \frac{2 - 2 41}{10}

Simplify the expression

More Steps

n = \frac{1 + 41}{5} n = \frac{2 - 2 41}{10}

Simplify the expression

More Steps

n = \frac{1 + 41}{5} n = \frac{1 - 41}{5}

Solution

n_{1} = \frac{1 - 41}{5}, n_{2} = \frac{1 + 41}{5}

Alternative Form

n_{1} \approx - 1.080625, n_{2} \approx 1.480625

Show Solution