(X+1)(x+2)=7x-1

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

(X+1)(X+2)=7X-1

We move all terms to the left:

(X+1)(X+2)-(7X-1)=0

We get rid of parentheses

(X+1)(X+2)-7X+1=0

We multiply parentheses ..

(+X^2+2X+X+2)-7X+1=0

We get rid of parentheses

X^2+2X+X-7X+2+1=0

We add all the numbers together, and all the variables

X^2-4X+3=0

a = 1; b = -4; c = +3;
Δ = b2-4ac
Δ = -42-4·1·3
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2}{2*1}=\frac{2}{2}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2}{2*1}=\frac{6}{2}
=3
$