100=-5(r-7)8r

Solution for 100=-5(r-7)8r equation:

100=-5(r-7)8r

We move all terms to the left:

100-(-5(r-7)8r)=0


We calculate terms in parentheses: -(-5(r-7)8r), so:

-5(r-7)8r

We multiply parentheses

-40r^2+280r

Back to the equation:

-(-40r^2+280r)


We get rid of parentheses

40r^2-280r+100=0

a = 40; b = -280; c = +100;
Δ = b2-4ac
Δ = -2802-4·40·100
Δ = 62400
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:

$\sqrt{\Delta}=\sqrt{62400}=\sqrt{1600*39}=\sqrt{1600}*\sqrt{39}=40\sqrt{39}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-40\sqrt{39}}{2*40}=\frac{280-40\sqrt{39}}{80}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+40\sqrt{39}}{2*40}=\frac{280+40\sqrt{39}}{80}
$