Question

2b^2-7=4b
I need help solving this

Answer 1

`b=(2\pm3√(2))/(2)`

Explanation:

Rearrange so the equation is in the general form of a quadratic equation
`ax^2+bx+c=0`

`\implies 2b^2-4b-7=0`

Replace b with x (we will change this back at the end, but this is to avoid confusion when using the quadratic formula):

`\implies 2x^2-4x-7=0`

Therefore, comparing the equation with
`ax^2+bx+c=0`

• a = 2
• b = -4
• c = -7

Use the quadratic formula to solve, inputting the above values:

`x=(-b\pm√(b^2-4ac) )/(2a)`

`\implies x=(-(-4)\pm√((-4)^2-4(2)(-7)) )/(2(2))`

`\implies x=(4\pm√(72))/(4)`

`\implies x=(4\pm6√(2))/(4)`

`\implies x=(2\pm3√(2))/(2)`

Finally, change x back to b:

`b=(2\pm3√(2))/(2)`