Question

What are the solutions to the equation 2x^2 + 9x =5

Answer 1

2x² + 9x = 5

2x² + 9x - 5 = 0

2x² + 10x - x - 5 = 0

2x(x + 5) - (x + 5) = 0

(2x - 1)(x + 5) = 0

2x - 1 = 0 => 2x₁ = 1 = > x₁ = 1/2

x + 5 = 0 => x₂ = - 5

Answer 2

`\displaystyle -5 \ and \ (1)/(2)`

Explanation:

`2x^2 + 9x =5`

we have to move 5 in the other side with a different sign, to get a 2 grade ecuation

`2x^2 + 9x -5= 0`

now we know

a=2

b=9

c=-5

we have to find delta

`\boxed{\Delta=b^2-4ac} \\\\ \Delta=9^2-4\cdot2\cdot(-5)\\ \Delta=81+40 \\ \Delta=121`

and now we have to use the formula to find the root square

`\displaystyle \boxed{ X_(1,2)=(-b\pm√(\Delta) )/(2a) }`

`\displaystyle X_1=(-b-√(\Delta) )/(2a) =(-9-11)/(2\cdot2)=(-20)/(4)  =-5`

`\displaystyle X_2=(-b+√(\Delta) )/(2a) =(-9+√(121) )/(2\cdot4) =(-9+11)/(4) =(2)/(4) =(1)/(2)`