On this webpage solving quadratic equations by quadratic formula we are going to learn how to solve quadratic equations by using quadratic formula.

(i) First we have to compare the given quadratic equation with the general form of quadratic equation ax² + bx + c = 0

(ii) Here the coefficient of x² is a, coefficient of x is b and the constant term is c.

(iii) Then we have to apply those values in the formula -b
± √ (b² - 4 a c)/2a

(i) x²- 7x + 12 = 0

Solution:

a = 1     b = -7    c = 12

= 8/2, 6/2

= 4, 3

(ii) 15x²- 11 x + 2 = 0

Solution:

a = 15   b = - 11     c = 2

= 12/30 ,   10/30

= 2/5 , 1/3

(iii) x + (1/x) = 2 ½

Solution:

(x² + 1)/x = 5/2

2 (x² + 1) = 5 x

2 x² + 2 = 5 x

2 x² - 5 x + 2 = 0

a = 2       b = -5      c = 2

x = 8/4 , 2/4

x = 2 , 1/2

(iv) 3 a²x² - ab x - 2b² = 0

a = 3 a²   b = - ab   c = - 2b²

x = 6ab/6a²  , -4ab/6a²

x = b/a , x = -2b/a

(v) a (x² + 1) =  x(a² + 1)

Solution:

a x² + a =  x(a² + 1)

a x² - x(a² + 1) + a = 0

a = a     b = -(a² + 1)   c = a

x = 2a²/2a , 2/2a

= a , 1/a

(vi) 36 x² - 12 a x + (a² - b²) =  0

a = 36        b = -12 a      c = (a² - b²)

x = (a + b)/6 , (a - b)/6

(vii) [(x - 1)/(x + 1)] + [(x - 3)/(x - 4)] = 10/3

Solution:

[(x - 1)(x - 4) + (x - 3)(x + 1)]/(x + 1)(x- 4) = 10/3

(x² - 5 x + 4 + x² - 2 x - 3)/(x² - 3 x - 4) = 10/3

3 (2x² - 7 x + 1) = 10(x² - 3 x - 4)

10 x² - 6 x² - 30 x + 21 x - 40 - 3 = 0

4 x² - 9 x - 43 = 0

(viii) a² x² + (a²- b²)x - b²= 0

Solution:

a = a²     b = (a²- b²)         c = - b²

x = 2b²/2a², -2a²/2a²

x = b²/a² , -1