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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-1)·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*-1}=\frac{-2}{-2}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*-1}=\frac{4}{-2}
=-2
$