Solve (2x - 3)/3 (4x)/3 = 7

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{3 - 3 15}{4}, x_{2} = \frac{3 + 3 15}{4}

Alternative Form

x_{1} \approx - 2.154738, x_{2} \approx 3.654738

Evaluate

\frac{2 x - 3}{3} \times \frac{4 x}{3} = 7

Multiply the terms

More Steps

\frac{4 x ( 2 x - 3 )}{9} = 7

Rewrite the expression

\frac{8}{9} x^{2} - \frac{4}{3} x = 7

Move the expression to the left side

\frac{8}{9} x^{2} - \frac{4}{3} x - 7 = 0

Multiply both sides

9 (\frac{8}{9} x^{2} - \frac{4}{3} x - 7) = 9 \times 0

Calculate

8 x^{2} - 12 x - 63 = 0

Substitute a= 8,b= - 12 and c= - 63 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 8 ( - 63 )}{2 \times 8}

Simplify the expression

x = \frac{12 \pm ( - 12 ) ^{2} - 4 \times 8 ( - 63 )}{16}

Simplify the expression

More Steps

x = \frac{12 \pm 2160}{16}

Simplify the radical expression

More Steps

x = \frac{12 \pm 12 15}{16}

Separate the equation into 2 possible cases

x = \frac{12 + 12 15}{16} x = \frac{12 - 12 15}{16}

Simplify the expression

More Steps

x = \frac{3 + 3 15}{4} x = \frac{12 - 12 15}{16}

Simplify the expression

More Steps

x = \frac{3 + 3 15}{4} x = \frac{3 - 3 15}{4}

Solution

x_{1} = \frac{3 - 3 15}{4}, x_{2} = \frac{3 + 3 15}{4}

Alternative Form

x_{1} \approx - 2.154738, x_{2} \approx 3.654738

Show Solution