31/2s+s+20=56

Solution for 31/2s+s+20=56 equation:

31/2s+s+20=56

We move all terms to the left:

31/2s+s+20-(56)=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+31/2s-36=0

We multiply all the terms by the denominator


s*2s-36*2s+31=0

Wy multiply elements

2s^2-72s+31=0

a = 2; b = -72; c = +31;
Δ = b2-4ac
Δ = -722-4·2·31
Δ = 4936
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:

$\sqrt{\Delta}=\sqrt{4936}=\sqrt{4*1234}=\sqrt{4}*\sqrt{1234}=2\sqrt{1234}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-2\sqrt{1234}}{2*2}=\frac{72-2\sqrt{1234}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+2\sqrt{1234}}{2*2}=\frac{72+2\sqrt{1234}}{4}
$