3x-(5x-3)=-x(-x-4)+1

Solution for 3x-(5x-3)=-x(-x-4)+1 equation:

3x-(5x-3)=-x(-x-4)+1

We move all terms to the left:

3x-(5x-3)-(-x(-x-4)+1)=0

We add all the numbers together, and all the variables

3x-(5x-3)-(-x(-1x-4)+1)=0

We get rid of parentheses

3x-5x-(-x(-1x-4)+1)+3=0


We calculate terms in parentheses: -(-x(-1x-4)+1), so:

-x(-1x-4)+1

We multiply parentheses

1x^2+4x+1

We add all the numbers together, and all the variables

x^2+4x+1

Back to the equation:

-(x^2+4x+1)


We add all the numbers together, and all the variables

-2x-(x^2+4x+1)+3=0

We get rid of parentheses

-x^2-2x-4x-1+3=0

We add all the numbers together, and all the variables

-1x^2-6x+2=0

a = -1; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·(-1)·2
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{11}}{2*-1}=\frac{6-2\sqrt{11}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{11}}{2*-1}=\frac{6+2\sqrt{11}}{-2}
$