Answer
The solutions are $x=-1$ and $x=\frac{4}{5}$.
Work Step by Step
The given equation is
$\Rightarrow 5x^2+x-4=0$
The equation is easily factorable. So, solve by factoring.
$\Rightarrow 5x^2+x-4=0$
Rewrite $x$ as $5x-4x$.
$\Rightarrow 5x^2+5x-4x-4=0$
Group the terms.
$\Rightarrow (5x^2+5x)+(-4x-4)=0$
Factor each group.
$\Rightarrow 5x(x+1)-4(x+1)=0$
Factor out $(x+1)$.
$\Rightarrow (x+1)(5x-4)=0$
Use zero-product property.
$\Rightarrow x+1=0$ or $5x-4=0$
Solve for $x$.
$\Rightarrow x=-1$ or $x=\frac{4}{5}$
Hence, the solutions are $x=-1$ and $x=\frac{4}{5}$.
