s+85=s2+38

Solution for s+85=s2+38 equation:

s+85=s2+38

We move all terms to the left:

s+85-(s2+38)=0

We add all the numbers together, and all the variables

-(+s^2+38)+s+85=0

We get rid of parentheses

-s^2+s-38+85=0

We add all the numbers together, and all the variables

-1s^2+s+47=0

a = -1; b = 1; c = +47;
Δ = b2-4ac
Δ = 12-4·(-1)·47
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-3\sqrt{21}}{2*-1}=\frac{-1-3\sqrt{21}}{-2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+3\sqrt{21}}{2*-1}=\frac{-1+3\sqrt{21}}{-2}
$