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s+3+1/2s+10=37
We move all terms to the left:
s+3+1/2s+10-(37)=0
Domain of the equation: 2s!=0We add all the numbers together, and all the variables
s!=0/2
s!=0
s∈R
s+1/2s-24=0
We multiply all the terms by the denominator
s*2s-24*2s+1=0
Wy multiply elements
2s^2-48s+1=0
a = 2; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·2·1
Δ = 2296
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}$$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2296}=\sqrt{4*574}=\sqrt{4}*\sqrt{574}=2\sqrt{574}$$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-2\sqrt{574}}{2*2}=\frac{48-2\sqrt{574}}{4} $$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+2\sqrt{574}}{2*2}=\frac{48+2\sqrt{574}}{4} $
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