s=21/2s+10=38

Solution for s=21/2s+10=38 equation:

s=21/2s+10=38

We move all terms to the left:

s-(21/2s+10)=0


Domain of the equation: 2s+10)!=0

s∈R


We get rid of parentheses

s-21/2s-10=0

We multiply all the terms by the denominator


s*2s-10*2s-21=0

Wy multiply elements

2s^2-20s-21=0

a = 2; b = -20; c = -21;
Δ = b2-4ac
Δ = -202-4·2·(-21)
Δ = 568
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:

$\sqrt{\Delta}=\sqrt{568}=\sqrt{4*142}=\sqrt{4}*\sqrt{142}=2\sqrt{142}$
$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{142}}{2*2}=\frac{20-2\sqrt{142}}{4}
$
$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{142}}{2*2}=\frac{20+2\sqrt{142}}{4}
$