SOLUTION: Solve this equation: {{{sqrt(7x-3)+3=2x}}}

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Question 611: Solve this equation:
sqrt%287x-3%29%2B3=2x

Found 2 solutions by arden42, Charles1947:
Answer by arden42(16) About Me  (Show Source):
You can put this solution on YOUR website!
Well, first we need to get rid of the sqare root. To do this, we need to get it on its own:
sqrt%287x-3%29=2x-3
Then square both sides:
7x-3=%282x-3%29%5E2
Expand the brackets:
7x-3=4x%5E2+-12x+%2B9
Get everything on one side:
4x%5E2-19x%2B12=0
In this case, the easiest way to solve it is to use the quadratic equation:
x+=+%2819+%2B-+sqrt%28+%28-19%29%5E2-4%2A4%2A12+%29%29%2F%282%2A4%29+
x+=+%2819+%2B-+sqrt%28+361+-+192+%29%29%2F8
x+=+%2819+%2B-+13%29%2F8
x+=+32%2F8%2C6%2F8
x+=+4%2C3%2F4

Answer by Charles1947(18) About Me  (Show Source):
You can put this solution on YOUR website!
If we subtract 3 from both sides of the equation we get
sqrt%287x-3%29=2x-3
To get rid of the radical we square both sides of the equation
7x-3=%282x%2B3%29x%282x-3%29=4x%5E2-12x%2B9
7x-3=4x%5E2-12x%2B9
Combine like terms
4x%5E2-19x%2B12=0
This is a quadratic equation so we will have 2 answers
Use the quadratic equation to solve
x+=+%2819+%2B-+sqrt%28+%28-19%29%5E2-4%2A4%2A12+%29%29%2F%282%2A4%29+
x+=+%2819+%2B-+sqrt%28+361+-+192+%29%29%2F8
x+=+%2819+%2B-+13%29%2F8
x+=+32%2F8and6%2F8
x+=+4and3%2F4