4(-x+2)-x-26=-23x-1-4(-2x-1)+x*x

Solution for 4(-x+2)-x-26=-23x-1-4(-2x-1)+x*x equation:

4(-x+2)-x-26=-23x-1-4(-2x-1)+x*x

We move all terms to the left:

4(-x+2)-x-26-(-23x-1-4(-2x-1)+x*x)=0

We add all the numbers together, and all the variables

4(-1x+2)-x-(-23x-1-4(-2x-1)+x*x)-26=0

We add all the numbers together, and all the variables

-1x+4(-1x+2)-(-23x-1-4(-2x-1)+x*x)-26=0

We multiply parentheses

-1x-4x-(-23x-1-4(-2x-1)+x*x)+8-26=0


We calculate terms in parentheses: -(-23x-1-4(-2x-1)+x*x), so:

-23x-1-4(-2x-1)+x*x

determiningTheFunctionDomain
-23x-4(-2x-1)+x*x-1

We multiply parentheses

-23x+8x+x*x+4-1

Wy multiply elements

x^2-23x+8x+4-1

We add all the numbers together, and all the variables

x^2-15x+3

Back to the equation:

-(x^2-15x+3)


We add all the numbers together, and all the variables

-5x-(x^2-15x+3)-18=0

We get rid of parentheses

-x^2-5x+15x-3-18=0

We add all the numbers together, and all the variables

-1x^2+10x-21=0

a = -1; b = 10; c = -21;
Δ = b2-4ac
Δ = 102-4·(-1)·(-21)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4}{2*-1}=\frac{-14}{-2}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*-1}=\frac{-6}{-2}
=+3
$