s-3+1/2s=11

Solution for s-3+1/2s=11 equation:

s-3+1/2s=11

We move all terms to the left:

s-3+1/2s-(11)=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+1/2s-14=0

We multiply all the terms by the denominator


s*2s-14*2s+1=0

Wy multiply elements

2s^2-28s+1=0

a = 2; b = -28; c = +1;
Δ = b2-4ac
Δ = -282-4·2·1
Δ = 776
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:

$\sqrt{\Delta}=\sqrt{776}=\sqrt{4*194}=\sqrt{4}*\sqrt{194}=2\sqrt{194}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{194}}{2*2}=\frac{28-2\sqrt{194}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{194}}{2*2}=\frac{28+2\sqrt{194}}{4}
$