Solve (2x-7)(4x-3)=112

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{17 - 3 113}{8}, x_{2} = \frac{17 + 3 113}{8}

Alternative Form

x_{1} \approx - 1.861305, x_{2} \approx 6.111305

Evaluate

(2 x - 7) (4 x - 3) = 112

Expand the expression

More Steps

8 x^{2} - 34 x + 21 = 112

Move the expression to the left side

8 x^{2} - 34 x - 91 = 0

Substitute a= 8,b= - 34 and c= - 91 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{34 \pm ( - 34 ) ^{2} - 4 \times 8 ( - 91 )}{2 \times 8}

Simplify the expression

x = \frac{34 \pm ( - 34 ) ^{2} - 4 \times 8 ( - 91 )}{16}

Simplify the expression

More Steps

x = \frac{34 \pm 4068}{16}

Simplify the radical expression

More Steps

x = \frac{34 \pm 6 113}{16}

Separate the equation into 2 possible cases

x = \frac{34 + 6 113}{16} x = \frac{34 - 6 113}{16}

Simplify the expression

More Steps

x = \frac{17 + 3 113}{8} x = \frac{34 - 6 113}{16}

Simplify the expression

More Steps

x = \frac{17 + 3 113}{8} x = \frac{17 - 3 113}{8}

Solution

x_{1} = \frac{17 - 3 113}{8}, x_{2} = \frac{17 + 3 113}{8}

Alternative Form

x_{1} \approx - 1.861305, x_{2} \approx 6.111305

Show Solution