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

Solution for x=-4x^2+5x+0 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-4x=0

a = 4; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·4·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*4}=\frac{8}{8}
=1
$