Question

6. 3x2 – 2x = 5
Quadratic formula

Answer 1

The solution to the quadratic equation be:

`x=(5)/(3),\:x=-1`

Explanation:

Given the expression

3x² – 2x = 5

Solving with the quadratic formula

`3x^2-2x=5`

subtract 5 from both sides

`3x^2-2x-5=5-5`

Simplify

`3x^2-2x-5=0`

For a quadratic equation of the form ax²+bx+c=0

`x_(1,\:2)=(-b\pm √(b^2-4ac))/(2a)`

For a = 3, b = -2, c = -5

`x_(1,\:2)=(-\left(-2\right)\pm √(\left(-2\right)^2-4\cdot \:3\left(-5\right)))/(2\cdot \:3)`

`x_(1,\:2)=(-\left(-2\right)\pm \:8)/(2\cdot \:3)`

Separate the solutions

`x_1=(-\left(-2\right)+8)/(2\cdot \:3),\:x_2=(-\left(-2\right)-8)/(2\cdot \:3)`

solving

`x_1=(-\left(-2\right)+8)/(2\cdot \:3)`

`=(2+8)/(2\cdot \:3)`

`=(10)/(6)`

`=(5)/(3)`

also solving

`x_2=(-\left(-2\right)-8)/(2\cdot \:3)`

`=(2-8)/(2\cdot \:3)`

`=(-6)/(2\cdot \:3)`

`=(-6)/(6)`

`=-(6)/(6)`

`=-1`

Therefore, the solution to the quadratic equation be:

`x=(5)/(3),\:x=-1`