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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


We calculate terms in parentheses: -((+2X^2+7X-2X-7)), so:

(+2X^2+7X-2X-7)

We get rid of parentheses

2X^2+7X-2X-7

We add all the numbers together, and all the variables

2X^2+5X-7

Back to the equation:

-(2X^2+5X-7)


We add all the numbers together, and all the variables

X-(2X^2+5X-7)-1=0

We get rid of parentheses

-2X^2+X-5X+7-1=0

We add all the numbers together, and all the variables

-2X^2-4X+6=0

a = -2; b = -4; c = +6;
Δ = b2-4ac
Δ = -42-4·(-2)·6
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-8}{2*-2}=\frac{-4}{-4}
=1
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+8}{2*-2}=\frac{12}{-4}
=-3
$