-2x-(x-7)(2x+1)=-x+(-5+1)+4x

Solution for -2x-(x-7)(2x+1)=-x+(-5+1)+4x equation:

-2x-(x-7)(2x+1)=-x+(-5+1)+4x

We move all terms to the left:

-2x-(x-7)(2x+1)-(-x+(-5+1)+4x)=0

We add all the numbers together, and all the variables

-2x-(x-7)(2x+1)-(-x+(-4)+4x)=0

We multiply parentheses ..

-(+2x^2+x-14x-7)-2x-(-x+(-4)+4x)=0


We calculate terms in parentheses: -(-x+(-4)+4x), so:

-x+(-4)+4x

determiningTheFunctionDomain
-x+4x+(-4)

We add all the numbers together, and all the variables

3x-4

Back to the equation:

-(3x-4)


We get rid of parentheses

-2x^2-x+14x-2x-3x+7+4=0

We add all the numbers together, and all the variables

-2x^2+8x+11=0

a = -2; b = 8; c = +11;
Δ = b2-4ac
Δ = 82-4·(-2)·11
Δ = 152
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:

$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{38}}{2*-2}=\frac{-8-2\sqrt{38}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{38}}{2*-2}=\frac{-8+2\sqrt{38}}{-4}
$