-x2+5x+3=x-1

Solution for -x2+5x+3=x-1 equation:

-x2+5x+3=x-1

We move all terms to the left:

-x2+5x+3-(x-1)=0

We add all the numbers together, and all the variables

-1x^2+5x-(x-1)+3=0

We get rid of parentheses

-1x^2+5x-x+1+3=0

We add all the numbers together, and all the variables

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

a = -1; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-1)·4
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{2}}{2*-1}=\frac{-4-4\sqrt{2}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{2}}{2*-1}=\frac{-4+4\sqrt{2}}{-2}
$