Solve 3/4x*x - 3/4*2/5x -1/2x +1/2*2/5=7

Question

Solve the quadratic equation

x_{1} = \frac{8 - 2 526}{15}, x_{2} = \frac{8 + 2 526}{15}

Alternative Form

x_{1} \approx - 2.524625, x_{2} \approx 3.591292

Evaluate

\frac{3}{4} x \times x - \frac{3}{4} \times \frac{2}{5} x - \frac{1}{2} x + \frac{1}{2} \times \frac{2}{5} = 7

Simplify

More Steps

\frac{3}{4} x^{2} - \frac{4}{5} x + \frac{1}{5} = 7

Move the expression to the left side

\frac{3}{4} x^{2} - \frac{4}{5} x - \frac{34}{5} = 0

Multiply both sides

20 (\frac{3}{4} x^{2} - \frac{4}{5} x - \frac{34}{5}) = 20 \times 0

Calculate

15 x^{2} - 16 x - 136 = 0

Substitute a= 15,b= - 16 and c= - 136 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{16 \pm ( - 16 ) ^{2} - 4 \times 15 ( - 136 )}{2 \times 15}

Simplify the expression

x = \frac{16 \pm ( - 16 ) ^{2} - 4 \times 15 ( - 136 )}{30}

Simplify the expression

More Steps

x = \frac{16 \pm 8416}{30}

Simplify the radical expression

More Steps

x = \frac{16 \pm 4 526}{30}

Separate the equation into 2 possible cases

x = \frac{16 + 4 526}{30} x = \frac{16 - 4 526}{30}

Simplify the expression

More Steps

x = \frac{8 + 2 526}{15} x = \frac{16 - 4 526}{30}

Simplify the expression

More Steps

x = \frac{8 + 2 526}{15} x = \frac{8 - 2 526}{15}

Solution

x_{1} = \frac{8 - 2 526}{15}, x_{2} = \frac{8 + 2 526}{15}

Alternative Form

x_{1} \approx - 2.524625, x_{2} \approx 3.591292

Show Solution