s+31/2s+10=45

Solution for s+31/2s+10=45 equation:

s+31/2s+10=45

We move all terms to the left:

s+31/2s+10-(45)=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-35=0

We multiply all the terms by the denominator


s*2s-35*2s+31=0

Wy multiply elements

2s^2-70s+31=0

a = 2; b = -70; c = +31;
Δ = b2-4ac
Δ = -702-4·2·31
Δ = 4652
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:

$\sqrt{\Delta}=\sqrt{4652}=\sqrt{4*1163}=\sqrt{4}*\sqrt{1163}=2\sqrt{1163}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1163}}{2*2}=\frac{70-2\sqrt{1163}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1163}}{2*2}=\frac{70+2\sqrt{1163}}{4}
$