s+22/1s+10=52

Solution for s+22/1s+10=52 equation:

s+22/1s+10=52

We move all terms to the left:

s+22/1s+10-(52)=0


Domain of the equation: 1s!=0

s∈R


We add all the numbers together, and all the variables

s+22/1s-42=0

We multiply all the terms by the denominator


s*1s-42*1s+22=0

Wy multiply elements

s^2-42s+22=0

a = 1; b = -42; c = +22;
Δ = b2-4ac
Δ = -422-4·1·22
Δ = 1676
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:

$\sqrt{\Delta}=\sqrt{1676}=\sqrt{4*419}=\sqrt{4}*\sqrt{419}=2\sqrt{419}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{419}}{2*1}=\frac{42-2\sqrt{419}}{2}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{419}}{2*1}=\frac{42+2\sqrt{419}}{2}
$