Solve 3a^2=3(8a-11)

Evaluate

3 a^{2} = 3 (8 a - 11)

Expand the expression

More Steps

3 a^{2} = 24 a - 33

Move the expression to the left side

3 a^{2} - 24 a + 33 = 0

Substitute a= 3,b= - 24 and c= 33 into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{24 \pm ( - 24 ) ^{2} - 4 \times 3 \times 33}{2 \times 3}

Simplify the expression

a = \frac{24 \pm ( - 24 ) ^{2} - 4 \times 3 \times 33}{6}

Simplify the expression

More Steps

a = \frac{24 \pm 180}{6}

Simplify the radical expression

More Steps

a = \frac{24 \pm 6 5}{6}

Separate the equation into 2 possible cases

a = \frac{24 + 6 5}{6} a = \frac{24 - 6 5}{6}

Simplify the expression

More Steps

a = 4 + 5 a = \frac{24 - 6 5}{6}

Simplify the expression

More Steps

a = 4 + 5 a = 4 - 5

Solution

a_{1} = 4 - 5, a_{2} = 4 + 5

Alternative Form

a_{1} \approx 1.763932, a_{2} \approx 6.236068

Solve the quadratic equation