7(x+1)-2x=x2-2x-3

Solution for 7(x+1)-2x=x2-2x-3 equation:

7(x+1)-2x=x2-2x-3

We move all terms to the left:

7(x+1)-2x-(x2-2x-3)=0

We add all the numbers together, and all the variables

-(+x^2-2x-3)+7(x+1)-2x=0

We add all the numbers together, and all the variables

-(+x^2-2x-3)-2x+7(x+1)=0

We multiply parentheses

-(+x^2-2x-3)-2x+7x+7=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+7x+10=0

a = -1; b = 7; c = +10;
Δ = b2-4ac
Δ = 72-4·(-1)·10
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{89}}{2*-1}=\frac{-7-\sqrt{89}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{89}}{2*-1}=\frac{-7+\sqrt{89}}{-2}
$