Question

6x²-7x=20 solve the following quadratic equation

Answer 1

`x1 = - (4)/(3)`

`x2 = (5)/(2)`

Explanation:

`6 {x}^(2) - 7x = 20`

Move constant to the left and change its sign

`{6x}^(2) - 7x - 20 = 0`

Write -7x as a difference

`6 {x}^(2) + 8x - 15x - 20 = 0`

Factor out 2x from the expression

`2x(3x + 4) - 15x - 20 = 0`

Factor out -5 from the expression

`2x(3x + 4) - 5(3x + 4) = 0`

Factor out 3x + 4 from the expression

`(3x + 4)(2x - 5) = 0`

When the product of factors equals 0 , at least one factor is 0

`3x + 4 = 0`

`2x - 5 = 0`

Solve the equation for X1

`3x + 4 = 0`

Move constant to right side and change its sign

`3x = 0 - 4`

Calculate the difference

`3x = - 4`

Divide both sides of the equation by 3

`(3x)/(3) = ( - 4)/(3)`

Calculate

`x = - (4)/(3)`

Again,

Solve for x2

`2x - 5 = 0`

Move constant to right side and change its sign

`2x = 0 + 5`

Calculate the sum

`2x = 5`

Divide both sides of the equation by 2

`(2x)/(2) = (5)/(2)`

Calculate

`x = (5)/(2)`

`x1 = - (4)/(3)`

`x2 = (5)/(2)`

Hope this helps...

Best regards!!

Answer 2

x = -4/3 and x = 5/2.

Explanation:

6x² - 7x = 20

6x² - 7x - 20 = 0

To solve this, we can use the quadratic formula to solve this.

[please ignore the A-hat; that is a bug]

`(-b±√(b^2 - 4ac) )/(2a)`

In this case, a = 6, b = -7, and c = -20.

`(-(-7)±√((-7)^2 - 4 * 6 * (-20)) )/(2(6))`

=
`(7±√(49 + 80 * 6) )/(12)`

=
`(7±√(49 + 480) )/(12)`

=
`(7±√(529) )/(12)`

=
`(7±23 )/(12)`

`(7 - 23 )/(12)` =
`(-16 )/(12)` = -8 / 6 = -4 / 3

`(7 + 23 )/(12)` =
`(30)/(12)` = 15 / 6 = 5 / 2

So, x = -4/3 and x = 5/2.

Hope this helps!