(6r+5)(3r-7)=1180

Solution for (6r+5)(3r-7)=1180 equation:

(6r+5)(3r-7)=1180

We move all terms to the left:

(6r+5)(3r-7)-(1180)=0

We multiply parentheses ..

(+18r^2-42r+15r-35)-1180=0

We get rid of parentheses

18r^2-42r+15r-35-1180=0

We add all the numbers together, and all the variables

18r^2-27r-1215=0

a = 18; b = -27; c = -1215;
Δ = b2-4ac
Δ = -272-4·18·(-1215)
Δ = 88209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{88209}=297$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-297}{2*18}=\frac{-270}{36}
=-7+1/2
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+297}{2*18}=\frac{324}{36}
=9
$