Solve -4d^21 = 5d - 42

Evaluate

- 4 d^{2} \times 1 = 5 d - 42

Multiply the terms

- 4 d^{2} = 5 d - 42

Move the expression to the left side

- 4 d^{2} - 5 d + 42 = 0

Multiply both sides

4 d^{2} + 5 d - 42 = 0

Substitute a= 4,b= 5 and c= - 42 into the quadratic formula d = \frac{- b \pm b ^{2} - 4 a c}{2 a}

d = \frac{- 5 \pm 5 ^{2} - 4 \times 4 ( - 42 )}{2 \times 4}

Simplify the expression

d = \frac{- 5 \pm 5 ^{2} - 4 \times 4 ( - 42 )}{8}

Simplify the expression

More Steps

d = \frac{- 5 \pm 697}{8}

Separate the equation into 2 possible cases

d = \frac{- 5 + 697}{8} d = \frac{- 5 - 697}{8}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

d = \frac{- 5 + 697}{8} d = - \frac{5 + 697}{8}

Solution

d_{1} = - \frac{5 + 697}{8}, d_{2} = \frac{- 5 + 697}{8}

Alternative Form

d_{1} \approx - 3.925095, d_{2} \approx 2.675095

Solve the quadratic equation