SOLUTION: solve the equation algebraically:{{{ sqrt( 5x+6 )= 2x-6 }}}

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Question 967588: solve the equation algebraically:+sqrt%28+5x%2B6+%29=+2x-6+
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

+sqrt%28+5x%2B6+%29=+2x-6+
+%28sqrt%28+5x%2B6+%29%29%5E2=+%282x-6%29%5E2+
+5x%2B6+=+%282x%29%5E2-24x%2B6%5E2+
+5x%2B6+=+4x%5E2-24x%2B36+
+0+=+4x%5E2-24x-5x-6%2B36+
+4x%5E2-29x%2B30=0+...factor completely, write -29x as -5x-24x
4x%5E2-5x-24x%2B30%29+=+0...group
%284x%5E2-5x%29-%2824x-30%29%29+=+0
x%284x-5%29-6%284x-5%29%29+=+0
%28x-6%29%284x-5%29+=+0
solutions:
if %28x-6%29+=+0=>x=6
if %284x-5%29+=+0=>4x=5=>x=5%2F4

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+50%2C+%28x-6%29%284x-5%29%29+