Solve (5x-3):(-2)=x^26

Question

Solve the quadratic equation

Solve by factoring

Solve using the quadratic formula

Solve using the PQ formula

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

Alternative Form

x_{1} = - 0.75, x_{2} = 0. \dot{3}

Evaluate

(5 x - 3) \div (- 2) = x^{2} \times 6

Divide the terms

More Steps

Evaluate

(5 x - 3) \div (- 2)

Rewrite the expression

\frac{5 x - 3}{- 2}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{5 x - 3}{2}

- \frac{5 x - 3}{2} = x^{2} \times 6

Use the commutative property to reorder the terms

- \frac{5 x - 3}{2} = 6 x^{2}

Swap the sides

6 x^{2} = - \frac{5 x - 3}{2}

Multiply both sides of the equation by LCD

6 x^{2} \times 2 = - \frac{5 x - 3}{2} \times 2

Simplify the equation

12 x^{2} = - \frac{5 x - 3}{2} \times 2

Simplify the equation

12 x^{2} = - 5 x + 3

Move the expression to the left side

12 x^{2} + 5 x - 3 = 0

Factor the expression

More Steps

Evaluate

12 x^{2} + 5 x - 3

Rewrite the expression

12 x^{2} + (9 - 4) x - 3

Calculate

12 x^{2} + 9 x - 4 x - 3

Rewrite the expression

3 x \times 4 x + 3 x \times 3 - 4 x - 3

Factor out 3 x from the expression

3 x (4 x + 3) - 4 x - 3

Factor out - 1 from the expression

3 x (4 x + 3) - (4 x + 3)

Factor out 4 x + 3 from the expression

(3 x - 1) (4 x + 3)

(3 x - 1) (4 x + 3) = 0

When the product of factors equals 0,at least one factor is 0

3 x - 1 = 0 4 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

3 x - 1 = 0

Move the constant to the right-hand side and change its sign

3 x = 0 + 1

Removing 0 doesn't change the value,so remove it from the expression

3 x = 1

Divide both sides

\frac{3 x}{3} = \frac{1}{3}

Divide the numbers

x = \frac{1}{3}

x = \frac{1}{3} 4 x + 3 = 0

Solve the equation for x

More Steps

Evaluate

4 x + 3 = 0

Move the constant to the right-hand side and change its sign

4 x = 0 - 3

Removing 0 doesn't change the value,so remove it from the expression

4 x = - 3

Divide both sides

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

Divide the numbers

x = \frac{- 3}{4}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

x = - \frac{3}{4}

x = \frac{1}{3} x = - \frac{3}{4}

Solution

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

Alternative Form

x_{1} = - 0.75, x_{2} = 0. \dot{3}

Show Solution