x^2+4x-1=x-4x^2

Solution for x^2+4x-1=x-4x^2 equation:

x^2+4x-1=x-4x^2

We move all terms to the left:

x^2+4x-1-(x-4x^2)=0

We get rid of parentheses

x^2+4x^2-x+4x-1=0

We add all the numbers together, and all the variables

5x^2+3x-1=0

a = 5; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·5·(-1)
Δ = 29
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{29}}{2*5}=\frac{-3-\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{29}}{2*5}=\frac{-3+\sqrt{29}}{10}
$