s+2-1/2s+10=52

Solution for s+2-1/2s+10=52 equation:

s+2-1/2s+10=52

We move all terms to the left:

s+2-1/2s+10-(52)=0


Domain of the equation: 2s!=0

s!=0/2

s!=0

s∈R


We add all the numbers together, and all the variables

s-1/2s-40=0

We multiply all the terms by the denominator


s*2s-40*2s-1=0

Wy multiply elements

2s^2-80s-1=0

a = 2; b = -80; c = -1;
Δ = b2-4ac
Δ = -802-4·2·(-1)
Δ = 6408
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:

$\sqrt{\Delta}=\sqrt{6408}=\sqrt{36*178}=\sqrt{36}*\sqrt{178}=6\sqrt{178}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-6\sqrt{178}}{2*2}=\frac{80-6\sqrt{178}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+6\sqrt{178}}{2*2}=\frac{80+6\sqrt{178}}{4}
$