7-9r(r+12)=25

Solution for 7-9r(r+12)=25 equation:

7-9r(r+12)=25

We move all terms to the left:

7-9r(r+12)-(25)=0

We add all the numbers together, and all the variables

-9r(r+12)-18=0

We multiply parentheses

-9r^2-108r-18=0

a = -9; b = -108; c = -18;
Δ = b2-4ac
Δ = -1082-4·(-9)·(-18)
Δ = 11016
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:

$\sqrt{\Delta}=\sqrt{11016}=\sqrt{324*34}=\sqrt{324}*\sqrt{34}=18\sqrt{34}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-18\sqrt{34}}{2*-9}=\frac{108-18\sqrt{34}}{-18}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+18\sqrt{34}}{2*-9}=\frac{108+18\sqrt{34}}{-18}
$