4x^2+2x=4-x

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

4x^2+2x=4-x

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2+3x-4=0

a = 4; b = 3; c = -4;
Δ = b2-4ac
Δ = 32-4·4·(-4)
Δ = 73
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{73}}{2*4}=\frac{-3-\sqrt{73}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{73}}{2*4}=\frac{-3+\sqrt{73}}{8}
$