-4r(r+7)=-75

Solution for -4r(r+7)=-75 equation:

-4r(r+7)=-75

We move all terms to the left:

-4r(r+7)-(-75)=0

We add all the numbers together, and all the variables

-4r(r+7)+75=0

We multiply parentheses

-4r^2-28r+75=0

a = -4; b = -28; c = +75;
Δ = b2-4ac
Δ = -282-4·(-4)·75
Δ = 1984
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:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-8\sqrt{31}}{2*-4}=\frac{28-8\sqrt{31}}{-8}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+8\sqrt{31}}{2*-4}=\frac{28+8\sqrt{31}}{-8}
$