What are the solutions to the equation 2abx^2-(b^2+6a^2)x+3ab=0 ?

The solutions to the equation 2abx^2-(b^2+6a^2)x+3ab=0 are x=(3a)/b ,x= b/(2a);\quad 2ab\ne 0

Find the zeros of 2abx^2-(b^2+6a^2)x+3ab=0

The zeros of 2abx^2-(b^2+6a^2)x+3ab=0 are x=(3a)/b ,x= b/(2a);\quad 2ab\ne 0

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2 ab x^{2} - (b^{2} + 6 a^{2}) x + 3 ab = 0

x = \frac{3 a}{b}, x = \frac{b}{2 a}; 2 ab \neq = 0

Solution steps

2 ab x^{2} - (b^{2} + 6 a^{2}) x + 3 ab = 0

Solve with the quadratic formula

x_{1, 2} = \frac{- ( - b ^{2} - 6 a ^{2} ) \pm ( - b ^{2} - 6 a ^{2} ) ^{2} - 4 \cdot 2 ab \cdot 3 ab}{2 \cdot 2 ab}

Simplify

(- b^{2} - 6 a^{2})^{2} - 4 \cdot 2 ab \cdot 3 ab : (6 a + b) (6 a - b)

x_{1, 2} = \frac{- ( - b ^{2} - 6 a ^{2} ) \pm ( 6 a + b ) ( 6 a - b )}{2 \cdot 2 ab}; 2 ab \neq = 0

Separate the solutions

x_{1} = \frac{- ( - b ^{2} - 6 a ^{2} ) + ( 6 a + b ) ( 6 a - b )}{2 \cdot 2 ab}, x_{2} = \frac{- ( - b ^{2} - 6 a ^{2} ) - ( 6 a + b ) ( 6 a - b )}{2 \cdot 2 ab}

x = \frac{- ( - b ^{2} - 6 a ^{2} ) + ( 6 a + b ) ( 6 a - b )}{2 \cdot 2 ab} : \frac{3 a}{b}

x = \frac{- ( - b ^{2} - 6 a ^{2} ) - ( 6 a + b ) ( 6 a - b )}{2 \cdot 2 ab} : \frac{b}{2 a}

The solutions to the quadratic equation are:

x = \frac{3 a}{b}, x = \frac{b}{2 a}; 2 ab \neq = 0

0 = - 4.9 t^{2} + 100 t + 20

- 1.86 x^{2} + 18.76 x + 1.21 = 10

(2 x - 5)^{2} = 4242

3 m (m - 1) - 9 = 2 m (m - 3) + 4

4 w^{2} + 12 w = - 9

What are the solutions to the equation 2abx^2-(b^2+6a^2)x+3ab=0 ?
The solutions to the equation 2abx^2-(b^2+6a^2)x+3ab=0 are x=(3a)/b ,x= b/(2a);\quad 2ab\ne 0
Find the zeros of 2abx^2-(b^2+6a^2)x+3ab=0
The zeros of 2abx^2-(b^2+6a^2)x+3ab=0 are x=(3a)/b ,x= b/(2a);\quad 2ab\ne 0