Solve 19v-4v^23=8v-19

Evaluate

19 v - 4 v^{2} \times 3 = 8 v - 19

Multiply the terms

19 v - 12 v^{2} = 8 v - 19

Move the expression to the left side

11 v - 12 v^{2} + 19 = 0

Rewrite in standard form

- 12 v^{2} + 11 v + 19 = 0

Multiply both sides

12 v^{2} - 11 v - 19 = 0

Substitute a= 12,b= - 11 and c= - 19 into the quadratic formula v = \frac{- b \pm b ^{2} - 4 a c}{2 a}

v = \frac{11 \pm ( - 11 ) ^{2} - 4 \times 12 ( - 19 )}{2 \times 12}

Simplify the expression

v = \frac{11 \pm ( - 11 ) ^{2} - 4 \times 12 ( - 19 )}{24}

Simplify the expression

More Steps

v = \frac{11 \pm 1033}{24}

Separate the equation into 2 possible cases

v = \frac{11 + 1033}{24} v = \frac{11 - 1033}{24}

Solution

v_{1} = \frac{11 - 1033}{24}, v_{2} = \frac{11 + 1033}{24}

Alternative Form

v_{1} \approx - 0.880847, v_{2} \approx 1.797513

Solve the quadratic equation