6s^2+57s+72=3

Solution for 6s^2+57s+72=3 equation:

6s^2+57s+72=3

We move all terms to the left:

6s^2+57s+72-(3)=0

We add all the numbers together, and all the variables

6s^2+57s+69=0

a = 6; b = 57; c = +69;
Δ = b2-4ac
Δ = 572-4·6·69
Δ = 1593
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1593}=\sqrt{9*177}=\sqrt{9}*\sqrt{177}=3\sqrt{177}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-3\sqrt{177}}{2*6}=\frac{-57-3\sqrt{177}}{12}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+3\sqrt{177}}{2*6}=\frac{-57+3\sqrt{177}}{12}
$