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I need help 5x2+5x-30=0

1 Answer

6 votes

Hello !

Answer:


\boxed{\sf x=2\ or\ x=-3}

Explanation:


\sf 5x^2+5x-30

This equation is a quadratic equation in the form ax²+bx+c=0

The solution of this equation is given by the quadratic formula :


\sf x=(-b\pm √(b^2-4ac))/(2a)

There are 3 cases depending on the values of the discriminant :


  • b^2-4ac > 0 : 2 real roots

  • b^2-4ac = 0 : no real root

  • b^2-4ac < 0 : no real root

Let's calculate the discriminant :


\sf b^2-4ac=5^2-4*5*(-30)=625 > 0

There are 2 real roots.

Now let's use the quadratic formula to find the two roots.


\sf x=(-5\pm√(5^2-4*5*(-30)))/(2*5)\\x=(-5\pm√(625))/(10) \\x_1=(-5+√(625))/(10)=2\\x_2=(-5-√(625))/(10)=-3\\\boxed{\sf x=2\ or\ x=-3}

Have a nice day ;)

User Makach
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