(2x+1)-(x+3)=(x^2-11)-(2x+1)

Solution for (2x+1)-(x+3)=(x^2-11)-(2x+1) equation:

(2x+1)-(x+3)=(x^2-11)-(2x+1)

We move all terms to the left:

(2x+1)-(x+3)-((x^2-11)-(2x+1))=0

We get rid of parentheses

2x-x-((x^2-11)-(2x+1))+1-3=0


We calculate terms in parentheses: -((x^2-11)-(2x+1)), so:

(x^2-11)-(2x+1)

We get rid of parentheses

x^2-2x-11-1

We add all the numbers together, and all the variables

x^2-2x-12

Back to the equation:

-(x^2-2x-12)


We add all the numbers together, and all the variables

x-(x^2-2x-12)-2=0

We get rid of parentheses

-x^2+x+2x+12-2=0

We add all the numbers together, and all the variables

-1x^2+3x+10=0

a = -1; b = 3; c = +10;
Δ = b2-4ac
Δ = 32-4·(-1)·10
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-7}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*-1}=\frac{4}{-2}
=-2
$