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

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

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

We move all terms to the left:

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

We multiply parentheses

4x-x*x+20-1=0

Wy multiply elements

-1x^2+4x+20-1=0

We add all the numbers together, and all the variables

-1x^2+4x+19=0

a = -1; b = 4; c = +19;
Δ = b2-4ac
Δ = 42-4·(-1)·19
Δ = 92
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:

$\sqrt{\Delta}=\sqrt{92}=\sqrt{4*23}=\sqrt{4}*\sqrt{23}=2\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{23}}{2*-1}=\frac{-4-2\sqrt{23}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{23}}{2*-1}=\frac{-4+2\sqrt{23}}{-2}
$