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+7/2S+10S=55
We move all terms to the left:
+7/2S+10S-(55)=0
Domain of the equation: 2S!=0We add all the numbers together, and all the variables
S!=0/2
S!=0
S∈R
10S+7/2S-55=0
We multiply all the terms by the denominator
10S*2S-55*2S+7=0
Wy multiply elements
20S^2-110S+7=0
a = 20; b = -110; c = +7;
Δ = b2-4ac
Δ = -1102-4·20·7
Δ = 11540
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}$$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{11540}=\sqrt{4*2885}=\sqrt{4}*\sqrt{2885}=2\sqrt{2885}$$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-110)-2\sqrt{2885}}{2*20}=\frac{110-2\sqrt{2885}}{40} $$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-110)+2\sqrt{2885}}{2*20}=\frac{110+2\sqrt{2885}}{40} $
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