s=3+1/2s+20=74

Solution for s=3+1/2s+20=74 equation:

s=3+1/2s+20=74

We move all terms to the left:

s-(3+1/2s+20)=0


Domain of the equation: 2s+20)!=0

s∈R


We add all the numbers together, and all the variables

s-(1/2s+23)=0

We get rid of parentheses

s-1/2s-23=0

We multiply all the terms by the denominator


s*2s-23*2s-1=0

Wy multiply elements

2s^2-46s-1=0

a = 2; b = -46; c = -1;
Δ = b2-4ac
Δ = -462-4·2·(-1)
Δ = 2124
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:

$\sqrt{\Delta}=\sqrt{2124}=\sqrt{36*59}=\sqrt{36}*\sqrt{59}=6\sqrt{59}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-6\sqrt{59}}{2*2}=\frac{46-6\sqrt{59}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+6\sqrt{59}}{2*2}=\frac{46+6\sqrt{59}}{4}
$