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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-4x^2+5x+8x-(4(x+2)-5x)=0


We calculate terms in parentheses: -(4(x+2)-5x), so:

4(x+2)-5x

We add all the numbers together, and all the variables

-5x+4(x+2)

We multiply parentheses

-5x+4x+8

We add all the numbers together, and all the variables

-1x+8

Back to the equation:

-(-1x+8)


We add all the numbers together, and all the variables

-4x^2+13x-(-1x+8)=0

We get rid of parentheses

-4x^2+13x+1x-8=0

We add all the numbers together, and all the variables

-4x^2+14x-8=0

a = -4; b = 14; c = -8;
Δ = b2-4ac
Δ = 142-4·(-4)·(-8)
Δ = 68
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{17}}{2*-4}=\frac{-14-2\sqrt{17}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{17}}{2*-4}=\frac{-14+2\sqrt{17}}{-8}
$