What are the solutions of $3 x^{2} + 14 x + 8 = 0$ $3x^2 + 14x + 8 = 0$ ?

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Answer 1 · 2016-03-13T05:01:16

$x = - \frac{2}{3}, - 4$ $x=-2/3,-4$

$3 x^{2} + 14 x + 8 = 0$ $color(blue)(3x^2+14x+8=0$

This is a Quadratic equation (in form $a x^{2} + b x + c = 0$ $ax^2+bx+c=0$ )

$x = \frac{- b \pm \sqrt{b^{2} - 4 a c}}{2 a}$ $color(brown)(x=(-b+-sqrt(b^2-4ac))/(2a)$

Where

$a = 3, b = 14, c = 8$ $color(red)(a=3,b=14,c=8$

Substitute the values in the formula

$\to x = \frac{- (14) \pm \sqrt{14^{2} - 4 (3) (8)}}{2 (3)}$ $rarrx=(-(14)+-sqrt(14^2-4(3)(8)))/(2(3))$

$\to x = \frac{- 14 \pm \sqrt{196 - 96}}{6}$ $rarrx=(-14+-sqrt(196-96))/(6)$

$\to x = \frac{- 14 \pm \sqrt{100}}{6}$ $rarrx=(-14+-sqrt100)/(6)$

$\to x = \frac{- 14 \pm 10}{6}$ $rarrcolor(orange)(x=(-14+-10)/(6)$

Now we have $2$ $2$ values for $x$ $x$

$1) x = \frac{- 14 + 10}{6} = - \frac{4}{6} = - \frac{2}{3}$ $color(indigo)(1))color(green)(x=(-14+10)/6=-4/6=-2/3$

$2) x = \frac{- 14 - 10}{6} = - \frac{24}{6} = - 4$ $color(indigo)(2))color(green)(x=(-14-10)/(6)=-24/6=-4$

What are the solutions of 3x2+14x+8=03x^2 + 14x + 8 = 0?