(x-1)(x+3)+6=4-x

Solution for (x-1)(x+3)+6=4-x equation:

(x-1)(x+3)+6=4-x

We move all terms to the left:

(x-1)(x+3)+6-(4-x)=0

We add all the numbers together, and all the variables

(x-1)(x+3)-(-1x+4)+6=0

We get rid of parentheses

(x-1)(x+3)+1x-4+6=0

We multiply parentheses ..

(+x^2+3x-1x-3)+1x-4+6=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

x^2+3x-1=0

a = 1; b = 3; c = -1;
Δ = b2-4ac
Δ = 32-4·1·(-1)
Δ = 13
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{13}}{2*1}=\frac{-3-\sqrt{13}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{13}}{2*1}=\frac{-3+\sqrt{13}}{2}
$