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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-5x=0

a = -1; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-1)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-1}=\frac{10}{-2}
=-5
$