SOLUTION: (sqrt(3)-2)*(5*sqrt(5)-x)=3*sqrt(3)-6

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Question 1000699: (sqrt(3)-2)*(5*sqrt(5)-x)=3*sqrt(3)-6
Found 2 solutions by Alan3354, MathTherapy:
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
(sqrt(3)-2)*(5*sqrt(5)-x)=3*sqrt(3)-6
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(5*sqrt(5)-x)=3*(sqrt(3)-2)/(sqrt(3)-2)
(5*sqrt(5)-x) = 3


Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation (in our case ) has the following solutons:



For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=36.0000000000002 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: -8.18033988749894, -14.180339887499. Here's your graph:

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The solver rounds off.
Answer by MathTherapy(10557)   (Show Source): You can put this solution on YOUR website!
(sqrt(3)-2)*(5*sqrt(5)-x)=3*sqrt(3)-6
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