Given that x^2:(3x+5) = 1:2 Find the possible values of x?

answers:
Jim Moor say: x²:(3x+5) = 1:2
x²/(3x+5) = 1/2
multiply by 2(3x+5) to both sides to maintain equality
2x² = 3x +5
2 x²  3 x  5 = 0
Factor, Complete the Square or use QF:
The left hand side factors into a product with two terms:
(x + 1) (2 x  5) = 0
Split into two equations:
x + 1 = 0 or 2 x  5 = 0
Subtract 1 from both sides:
x = 1
2 x  5 = 0
Add 5 to both sides:
x = 1 or 2 x = 5
Divide both sides by 2:
Answer: x = 1 or x = 5/2

alex say: x^2/(3x + 5) = 1/2
solve for x

Mike G say: 2x^23x5 = 0
(2x5)(x+1) = 0
x = 1 or 2.5

Iggy Rocko say: x^2/(3x + 5) = 1/2
2x^2 = 3x + 5
2x^2  3x  5 = 0
(2x  5)(x + 1) = 0
x = 5/2 or x = 1

Como say: 
x² / (3x + 5) = 1/2
2x² = 3x + 5
2x²  3x  5 = 0
( 2x  5 ) ( x + 1 ) = 0
x = 5/2 , x =  1

Puzzling say: Change the ratio into divisions:
x² / (3x + 5) = 1 / 2
Cross multiply:
2x² = 3x + 5
Get everything on one side:
2x²  3x  5 = 0
Factor:
(2x  5)(x + 1) = 0
By the zero product rule, if ab = 0, then a=0 or b=0:
2x  5 = 0
2x = 5
x = 5/2
x = 2½
or
x + 1 = 0
x = 1
Doublecheck both answers make sense:
(2.5)² = 6.25 and 3(2.5) + 5 = 12.5
6.25 / 12.5 = 1 / 2
(1)² = 1 and 3(1) + 5 = 2
1 / 2 = 1 / 2
Answer:
x = 2.5 or x = 1

Captain Matticus, LandPiratesInc say: 2 * x^2 = 1 * (3x + 5)
2x^2  3x  5 = 0
x = (3 +/ sqrt(9 + 40)) / 4
x = (3 +/ 7) / 4
x = 10/4 , 4/4
x = 2.5 , 1
2.5^2 = 6.25
3 * 2.5 + 5 = 7.5 + 5 = 12.5
6.25 / 12.5 = 1/2
(1)^2 / (3 * (1) + 5) =>
1 / (3 + 5) =>
1/2
Both work
