(r+6)(r)-374=0

Solution for (r+6)(r)-374=0 equation:

(r+6)(r)-374=0

We multiply parentheses

r^2+6r-374=0

a = 1; b = 6; c = -374;
Δ = b2-4ac
Δ = 62-4·1·(-374)
Δ = 1532
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:

$\sqrt{\Delta}=\sqrt{1532}=\sqrt{4*383}=\sqrt{4}*\sqrt{383}=2\sqrt{383}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{383}}{2*1}=\frac{-6-2\sqrt{383}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{383}}{2*1}=\frac{-6+2\sqrt{383}}{2}
$