4x-2x(x-2)=-4+5x-13

Solution for 4x-2x(x-2)=-4+5x-13 equation:

4x-2x(x-2)=-4+5x-13

We move all terms to the left:

4x-2x(x-2)-(-4+5x-13)=0

We add all the numbers together, and all the variables

4x-2x(x-2)-(5x-17)=0

We multiply parentheses

-2x^2+4x+4x-(5x-17)=0

We get rid of parentheses

-2x^2+4x+4x-5x+17=0

We add all the numbers together, and all the variables

-2x^2+3x+17=0

a = -2; b = 3; c = +17;
Δ = b2-4ac
Δ = 32-4·(-2)·17
Δ = 145
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{145}}{2*-2}=\frac{-3-\sqrt{145}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{145}}{2*-2}=\frac{-3+\sqrt{145}}{-4}
$