Solve this equation using the quadratic formula.

3x^2 -5 = -8x -10

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Solve `3x^2-5=-8x-10` using the quadratic formula:

The quadratic formula is : if `ax^2+bx+c=0 "then" x=(-b+-sqrt(b^2-4ac))/(2a)`

We must rewrite in standard form:

`3x^2+8x+5=0` Now a=3,b=8, and c=5 so:

`x=(-8+-sqrt(8^2-4(3)(5)))/(2(3))`

`=(-8+-sqrt(4))/6`

`=-4/3+1/3=-1`

or

`=-4/3-1/3=-5/3`

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The solutions are `x=-1,-5/3`

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You could factor:

`3x^2+8x+5=(3x+5)(x+1)` and find the roots that way also.

`3x^2-5=-8x-10`

`3x^2+8x+5=0`

`3x^2+3x+5x+5=0`

`3x(x+1)+5(x+1)=0`

`(3x+5)(x+1)=0`

`3x+5=0 rArr x=-5/3`

`x+1=0 rArr x=-1`

So solutions are `x_1=-1` ; `x_2=-5/3`

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