-7+6r=5r-r(2r+4)

Solution for -7+6r=5r-r(2r+4) equation:

-7+6r=5r-r(2r+4)

We move all terms to the left:

-7+6r-(5r-r(2r+4))=0


We calculate terms in parentheses: -(5r-r(2r+4)), so:

5r-r(2r+4)

We multiply parentheses

-2r^2+5r-4r

We add all the numbers together, and all the variables

-2r^2+r

Back to the equation:

-(-2r^2+r)


We get rid of parentheses

2r^2-r+6r-7=0

We add all the numbers together, and all the variables

2r^2+5r-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:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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