Question

What is the solution of the quadratic equation below?

4x^2 - 30x + 45 = 0

Answer 1

5.43 , 2.07

Explanation:

The given quadratic equation is

`\[4x^(2)-30x+45=0\]`

This is of the form
`\[ax^(2)+bx+c=0\]`

where,

a=4

b=-30

c=45

Roots of the quadratic equation of this form are given by:

`\[\frac{-b\pm \sqrt{b^(2)-4ac}}{2a}\]`

Substituting the values of a,b,c in the formula:

`\[\frac{-(-30)\pm \sqrt{(-30)^(2)-4*4*45}}{2*4}\]`

=
`\[(30\pm √(900-720))/(8)\]`

=
`\[(30\pm √(900-720))/(8)\]`

=
`\[(30\pm √(180))/(8)\]`

=
`\[(30\pm 13.416)/(8)\]`

=5.43,2.07

Answer 2

Explanation:

The general form of a quadratic equation is

ax^2 + b^2 + c

The given quadratic equation is

4x^2 - 30x + 45 = 0.

To find the solutions, we will apply the general formula for solving quadratic equations. It is expressed as

x = [-b ±√(b^2 - 4ac)]/2a

From the given quadratic equation,

a = 4

b = - 30

c = 45

Therefore,

x = [- - 30 ±√(- 30^2 - 4 × 4 × 45)]/2×4

x = [30 ±√(900 - 768)]/8

x = [30 ±√132]/8

x = [30 ± 11.5]/8

x = [30 + 11.5]/8 or x = [30 - 11.5]/8

x = 41.5/8 or x = 18.5/8

x = 5.1875 or x = 2.3125