Question 972553
number is x

2x^2 +7x=15
2x^2-7x-15=0  I moved the 15 over to make it a quadratic equation =0
(2x-3) (x+5)=0  factoring, using 5 and 3.
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x=(3/2), -5
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Check -5:  50 -35=15
Check (3/2) :  (9/2) +(21/2)=(30/2)=15
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Number =x
2x^2=5x+17
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do same thing
2x^2-5x-17=0
Try quadratic formula
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(1/4) (5+/- sqrt (25+136))  This is the exact form of x: {-5 +/- sqrt (161)}/4
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sqrt (161)=12.69
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(1/4) 17.69=4.42
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(1/4) (-7.69)=-1.92 ;  x=-1.92,4.42 decimal
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4.42^2 =19.53
twice that is 39.06
-5x=-22.1
-17 gets to 39.06 ;with rounding

(-1.92^2)*2=7.37
-5(-1.92)=9.6
9.6-17=-7.4  close enough with rounding
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x is one number
x+3 the other
x^2 +x^2 +6x+9    ; (that is (x+3)(x+3)   =269
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2x^2+6x -260=0
x^2+3x-130=0  , dividing by 2.
(x+13)(x-10)=0
one number is 10, the other is 13
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squared 10=100
square 13=169
sum is 269

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One number is -13, the other is -10
They do the same thing.  You need both solutions.