Solve 6a^2-67a+231/4=0

Evaluate

6 a^{2} - 67 a + \frac{231}{4} = 0

Multiply both sides

4 (6 a^{2} - 67 a + \frac{231}{4}) = 4 \times 0

Calculate

24 a^{2} - 268 a + 231 = 0

Substitute a= 24,b= - 268 and c= 231 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{268 \pm ( - 268 ) ^{2} - 4 \times 24 \times 231}{2 \times 24}

Simplify the expression

a = \frac{268 \pm ( - 268 ) ^{2} - 4 \times 24 \times 231}{48}

Simplify the expression

More Steps

a = \frac{268 \pm 26 8 ^{2} - 22176}{48}

Simplify the radical expression

More Steps

a = \frac{268 \pm 4 3103}{48}

Separate the equation into 2 possible cases

a = \frac{268 + 4 3103}{48} a = \frac{268 - 4 3103}{48}

Simplify the expression

More Steps

a = \frac{67 + 3103}{12} a = \frac{268 - 4 3103}{48}

Simplify the expression

More Steps

a = \frac{67 + 3103}{12} a = \frac{67 - 3103}{12}

Solution

a_{1} = \frac{67 - 3103}{12}, a_{2} = \frac{67 + 3103}{12}

Alternative Form

a_{1} \approx 0.941285, a_{2} \approx 10.225381

Solve the quadratic equation