=(r+7)(r-2)

Solution for =(r+7)(r-2) equation:

=(r+7)(r-2)

We move all terms to the left:

-((r+7)(r-2))=0

We multiply parentheses ..

-((+r^2-2r+7r-14))=0


We calculate terms in parentheses: -((+r^2-2r+7r-14)), so:

(+r^2-2r+7r-14)

We get rid of parentheses

r^2-2r+7r-14

We add all the numbers together, and all the variables

r^2+5r-14

Back to the equation:

-(r^2+5r-14)


We get rid of parentheses

-r^2-5r+14=0

We add all the numbers together, and all the variables

-1r^2-5r+14=0

a = -1; b = -5; c = +14;
Δ = b2-4ac
Δ = -52-4·(-1)·14
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*-1}=\frac{-4}{-2}
=+2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*-1}=\frac{14}{-2}
=-7
$