1-4(2x+1)=x*x+4

Solution for 1-4(2x+1)=x*x+4 equation:

1-4(2x+1)=x*x+4

We move all terms to the left:

1-4(2x+1)-(x*x+4)=0

We multiply parentheses

-8x-(x*x+4)-4+1=0

We get rid of parentheses

-8x-x*x-4-4+1=0

We add all the numbers together, and all the variables

-8x-x*x-7=0

Wy multiply elements

-1x^2-8x-7=0

a = -1; b = -8; c = -7;
Δ = b2-4ac
Δ = -82-4·(-1)·(-7)
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-6}{2*-1}=\frac{2}{-2}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+6}{2*-1}=\frac{14}{-2}
=-7
$