Solve 3*(4-x) 2*(3x-2)=-5

Question

Solve the quadratic equation

Solve using the quadratic formula

Solve by completing the square

Solve using the PQ formula

x_{1} = \frac{14 - 110}{6}, x_{2} = \frac{14 + 110}{6}

Alternative Form

x_{1} \approx 0.585319, x_{2} \approx 4.081348

Evaluate

3 (4 - x) \times 2 (3 x - 2) = - 5

Multiply the terms

6 (4 - x) (3 x - 2) = - 5

Expand the expression

More Steps

84 x - 48 - 18 x^{2} = - 5

Move the expression to the left side

84 x - 43 - 18 x^{2} = 0

Rewrite in standard form

- 18 x^{2} + 84 x - 43 = 0

Multiply both sides

18 x^{2} - 84 x + 43 = 0

Substitute a= 18,b= - 84 and c= 43 into the quadratic formula x = \frac{- b \pm b ^{2} - 4 a c}{2 a}

x = \frac{84 \pm ( - 84 ) ^{2} - 4 \times 18 \times 43}{2 \times 18}

Simplify the expression

x = \frac{84 \pm ( - 84 ) ^{2} - 4 \times 18 \times 43}{36}

Simplify the expression

More Steps

x = \frac{84 \pm 3960}{36}

Simplify the radical expression

More Steps

x = \frac{84 \pm 6 110}{36}

Separate the equation into 2 possible cases

x = \frac{84 + 6 110}{36} x = \frac{84 - 6 110}{36}

Simplify the expression

More Steps

x = \frac{14 + 110}{6} x = \frac{84 - 6 110}{36}

Simplify the expression

More Steps

x = \frac{14 + 110}{6} x = \frac{14 - 110}{6}

Solution

x_{1} = \frac{14 - 110}{6}, x_{2} = \frac{14 + 110}{6}

Alternative Form

x_{1} \approx 0.585319, x_{2} \approx 4.081348

Show Solution