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

Evaluate

\frac{x ^{2}}{3} - \frac{x - 1}{2} = 1

Multiply both sides of the equation by LCD

(\frac{x ^{2}}{3} - \frac{x - 1}{2}) \times 6 = 1 \times 6

Simplify the equation

More Steps

2 x^{2} - 3 x + 3 = 1 \times 6

Any expression multiplied by 1 remains the same

2 x^{2} - 3 x + 3 = 6

Move the expression to the left side

2 x^{2} - 3 x + 3 - 6 = 0

Subtract the numbers

2 x^{2} - 3 x - 3 = 0

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

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

Simplify the expression

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

Simplify the expression

More Steps

x = \frac{3 \pm 33}{4}

Separate the equation into 2 possible cases

x = \frac{3 + 33}{4} x = \frac{3 - 33}{4}

Solution

x_{1} = \frac{3 - 33}{4}, x_{2} = \frac{3 + 33}{4}

Alternative Form

x_{1} \approx - 0.686141, x_{2} \approx 2.186141

(x^2)/3 (x 1)/2 =1