37+s=80/2s=13

Solution for 37+s=80/2s=13 equation:

37+s=80/2s=13

We move all terms to the left:

37+s-(80/2s)=0


Domain of the equation: 2s)!=0

s!=0/1

s!=0

s∈R


We add all the numbers together, and all the variables

s-(+80/2s)+37=0

We get rid of parentheses

s-80/2s+37=0

We multiply all the terms by the denominator


s*2s+37*2s-80=0

Wy multiply elements

2s^2+74s-80=0

a = 2; b = 74; c = -80;
Δ = b2-4ac
Δ = 742-4·2·(-80)
Δ = 6116
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:

$\sqrt{\Delta}=\sqrt{6116}=\sqrt{4*1529}=\sqrt{4}*\sqrt{1529}=2\sqrt{1529}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-2\sqrt{1529}}{2*2}=\frac{-74-2\sqrt{1529}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+2\sqrt{1529}}{2*2}=\frac{-74+2\sqrt{1529}}{4}
$