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

Solution for 0=(x-1)(2x+7) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+2x^2+7x-2x-7))=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 get rid of parentheses

-2x^2-5x+7=0

a = -2; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-2)·7
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*-2}=\frac{14}{-4}
=-3+1/2
$