Question

if 5x+7/2=3/2x-14then x?​

Answer 1

Answer:

5x+7/2=3/2x-14

By rationalizing L. H. S

10x+7/2=3/2x-14

Cross multiplying

(10x+7) (2x-14) = 3×2

10x(2x-14) 7 (2x-14) = 6

20x^2-140x+14x-98 = 6

20x^2-126x-98=6

By using Quadratic equation

Answer 2

Step-by-step explanation:

     5x+7/2 = 3/2x-14

or, (10x+7)/2 = (3-28x)/2x

or, 2x(10x+7) = 2(3-28x)

or, 20x²+14x = 6-56x

or, 20x²+70x = 6

or, 20x²+70x-6 = 0

or, 2(10x²+35x-3) = 0

or, 10x²+35x-3 = 0

By the Quadratic formula,

we know that, D = b²-4ac

                           = (35)²-4(10)(-3)

                           = 1225 + 120 = 1345

Now, x = (-b±√D)/2a

           = (-35±√1345)/2(10)

       (-35+√1345)/20              |         (-35-√1345)/20

  =  (-35+5√269)/20              |     =  (-35-5√269)/20

  =  5(-7+√269)/20                |     =  5(-7-5√269)/20

  = (-7+√269)/4                      |     =  (-7-√269)/4

Therefore, the two roots of the given equation are (-7+√269)/4 and (-7-√269)/40

                                       Hope, it will help you.......