5x=3x-4x^2

Solution for 5x=3x-4x^2 equation:

5x=3x-4x^2

We move all terms to the left:

5x-(3x-4x^2)=0

We get rid of parentheses

4x^2-3x+5x=0

We add all the numbers together, and all the variables

4x^2+2x=0

a = 4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*4}=\frac{0}{8}
=0
$