Solve 3/4x^2 - 3/2x 1 = (b 1)3

Question

Solve the equation

Solve for x

Solve for b

x = 1 + 1 + 4 b x = 1 - 1 + 4 b

Evaluate

\frac{3}{4} x^{2} - \frac{3}{2} x \times 1 = (b \times 1) \times 3

Remove the parentheses

\frac{3}{4} x^{2} - \frac{3}{2} x \times 1 = b \times 1 \times 3

Multiply the terms

\frac{3}{4} x^{2} - \frac{3}{2} x = b \times 1 \times 3

Multiply the terms

More Steps

\frac{3}{4} x^{2} - \frac{3}{2} x = 3 b

Move the expression to the left side

\frac{3}{4} x^{2} - \frac{3}{2} x - 3 b = 0

Multiply both sides

4 (\frac{3}{4} x^{2} - \frac{3}{2} x - 3 b) = 4 \times 0

Calculate

3 x^{2} - 6 x - 12 b = 0

Substitute a= 3,b= - 6 and c= - 12 b into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 3 ( - 12 b )}{2 \times 3}

Simplify the expression

x = \frac{6 \pm ( - 6 ) ^{2} - 4 \times 3 ( - 12 b )}{6}

Simplify the expression

More Steps

x = \frac{6 \pm 36 + 144 b}{6}

Simplify the radical expression

More Steps

x = \frac{6 \pm 6 1 + 4 b}{6}

Separate the equation into 2 possible cases

x = \frac{6 + 6 1 + 4 b}{6} x = \frac{6 - 6 1 + 4 b}{6}

Simplify the expression

More Steps

x = 1 + 1 + 4 b x = \frac{6 - 6 1 + 4 b}{6}

Solution

More Steps

x = 1 + 1 + 4 b x = 1 - 1 + 4 b

Show Solution