Solve b(b-1) = a(2a-1)

Evaluate

b (b - 1) = a (2 a - 1)

Rewrite the expression

b^{2} - b = a (2 a - 1)

Swap the sides of the equation

a (2 a - 1) = b^{2} - b

Expand the expression

More Steps

2 a^{2} - a = b^{2} - b

Move the expression to the left side

2 a^{2} - a - (b^{2} - b) = 0

If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses

2 a^{2} - a - b^{2} + b = 0

Substitute a= 2,b= - 1 and c= - b^{2} + b into the quadratic formula a = \frac{- b \pm b ^{2} - 4 a c}{2 a}

a = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 2 ( - b ^{2} + b )}{2 \times 2}

Simplify the expression

a = \frac{1 \pm ( - 1 ) ^{2} - 4 \times 2 ( - b ^{2} + b )}{4}

Simplify the expression

More Steps

a = \frac{1 \pm 1 + 8 b ^{2} - 8 b}{4}

Solution

a = \frac{1 + 1 + 8 b ^{2} - 8 b}{4} a = \frac{1 - 1 + 8 b ^{2} - 8 b}{4}

Solve the equation