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

Solution for 4x-2x(x-5)=4+5x-4 equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-2x^2+4x+10x-(+5x)=0

We get rid of parentheses

-2x^2+4x+10x-5x=0

We add all the numbers together, and all the variables

-2x^2+9x=0

a = -2; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-2)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-2}=\frac{-18}{-4}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-2}=\frac{0}{-4}
=0
$