SOLUTION: Find the real or imaginary solutions of each equation by factoring. 6x^2+13x-5=0

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Question 687620: Find the real or imaginary solutions of each equation by factoring.
6x^2+13x-5=0
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+6x%5E2%2B13x-5=0+
Use the quadratic formula when the equation
is in the form +a%2Ax%5E2+%2B+b%2Ax+%2B+c+=+0+
+x+=+%28-b+%2B-+sqrt%28+b%5E2+-+4%2Aa%2Ac+%29%29+%2F+%282%2Aa%29+
+a+=+6+
+b+=+13+
+c+=+-5+
+x+=+%28-13+%2B-+sqrt%28+13%5E2+-+4%2A6%2A%28-5%29+%29%29+%2F+%282%2A6%29+
+x+=+%28-13+%2B-+sqrt%28+169+%2B120+%29%29+%2F+12+
+x+=+%28-13+%2B-+sqrt%28+289+%29%29+%2F+12+
+x+=+%28-13+%2B-+17+%29+%2F+12+
+x+=+%28+-13+%2B+17+%29+%2F+12+
+x+=+4%2F12+
(1) +x+=+1%2F3+
and, also,
+x+=+%28+-13+-+17+%29+%2F+12+
+x+=+-30%2F12+
(2) +x+=+-5%2F2+
----------------
Now rewrite (1) and (2) as:
(1) +x+-+1%2F3+=+0+
(2) +x+%2B+5%2F2+=+0+
Now multiply both sides of (1) by +3+
and both sides of (2) by +2+
(1) +3x+-+1+=+0+
(2) +2x+%2B+5+=+0+
So, the factoring is:
+%28+3x+-+1+%29%2A%28+2x+%2B+5+%29+=+0+
check:
+6x%5E2+-+2x+%2B+15x+-+5+=+0+
+6%5E2+%2B+13x+-+5+=+0+
OK