-40=7(-2r+2)4r

Solution for -40=7(-2r+2)4r equation:

-40=7(-2r+2)4r

We move all terms to the left:

-40-(7(-2r+2)4r)=0


We calculate terms in parentheses: -(7(-2r+2)4r), so:

7(-2r+2)4r

We multiply parentheses

-56r^2+56r

Back to the equation:

-(-56r^2+56r)


We get rid of parentheses

56r^2-56r-40=0

a = 56; b = -56; c = -40;
Δ = b2-4ac
Δ = -562-4·56·(-40)
Δ = 12096
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{12096}=\sqrt{576*21}=\sqrt{576}*\sqrt{21}=24\sqrt{21}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-24\sqrt{21}}{2*56}=\frac{56-24\sqrt{21}}{112}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+24\sqrt{21}}{2*56}=\frac{56+24\sqrt{21}}{112}
$