Question

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

Answer 1

Answer:

$\displaystyle -5 \ and \ \frac{1}{2}$

Step-by-step 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

$\displaystyle \boxed{ X_{1,2}=\frac{-b\pm\sqrt{\Delta} }{2a} }$

$\displaystyle X_1=\frac{-b-\sqrt{\Delta} }{2a} =\frac{-9-11}{2\cdot2}=\frac{-20}{4} =-5$

$\displaystyle X_2=\frac{-b+\sqrt{\Delta} }{2a} =\frac{-9+\sqrt{121} }{2\cdot4} =\frac{-9+11}{4} =\frac{2}{4} =\frac{1}{2}$

Answer 2

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