-5x(x+2)=-(-5x+1)-x

Solution for -5x(x+2)=-(-5x+1)-x equation:

-5x(x+2)=-(-5x+1)-x

We move all terms to the left:

-5x(x+2)-(-(-5x+1)-x)=0

We multiply parentheses

-5x^2-10x-(-(-5x+1)-x)=0


We calculate terms in parentheses: -(-(-5x+1)-x), so:

-(-5x+1)-x

We add all the numbers together, and all the variables

-1x-(-5x+1)

We get rid of parentheses

-1x+5x-1

We add all the numbers together, and all the variables

4x-1

Back to the equation:

-(4x-1)


We get rid of parentheses

-5x^2-10x-4x+1=0

We add all the numbers together, and all the variables

-5x^2-14x+1=0

a = -5; b = -14; c = +1;
Δ = b2-4ac
Δ = -142-4·(-5)·1
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-6\sqrt{6}}{2*-5}=\frac{14-6\sqrt{6}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+6\sqrt{6}}{2*-5}=\frac{14+6\sqrt{6}}{-10}
$