Solve 3/5 * (5x-2)^2 - 12 = 0

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{2 - 2 5}{5}, x_{2} = \frac{2 + 2 5}{5}

Alternative Form

x_{1} \approx - 0.494427, x_{2} \approx 1.294427

Evaluate

\frac{3}{5} (5 x - 2)^{2} - 12 = 0

Expand the expression

More Steps

15 x^{2} - 12 x - \frac{48}{5} = 0

Multiply both sides

5 (15 x^{2} - 12 x - \frac{48}{5}) = 5 \times 0

Calculate

75 x^{2} - 60 x - 48 = 0

Substitute a= 75,b= - 60 and c= - 48 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{60 \pm ( - 60 ) ^{2} - 4 \times 75 ( - 48 )}{2 \times 75}

Simplify the expression

x = \frac{60 \pm ( - 60 ) ^{2} - 4 \times 75 ( - 48 )}{150}

Simplify the expression

More Steps

x = \frac{60 \pm 18000}{150}

Simplify the radical expression

More Steps

x = \frac{60 \pm 60 5}{150}

Separate the equation into 2 possible cases

x = \frac{60 + 60 5}{150} x = \frac{60 - 60 5}{150}

Simplify the expression

More Steps

x = \frac{2 + 2 5}{5} x = \frac{60 - 60 5}{150}

Simplify the expression

More Steps

x = \frac{2 + 2 5}{5} x = \frac{2 - 2 5}{5}

Solution

x_{1} = \frac{2 - 2 5}{5}, x_{2} = \frac{2 + 2 5}{5}

Alternative Form

x_{1} \approx - 0.494427, x_{2} \approx 1.294427

Show Solution