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(S)=1/2S+30
We move all terms to the left:
(S)-(1/2S+30)=0
Domain of the equation: 2S+30)!=0We get rid of parentheses
S∈R
S-1/2S-30=0
We multiply all the terms by the denominator
S*2S-30*2S-1=0
Wy multiply elements
2S^2-60S-1=0
a = 2; b = -60; c = -1;
Δ = b2-4ac
Δ = -602-4·2·(-1)
Δ = 3608
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}$$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3608}=\sqrt{4*902}=\sqrt{4}*\sqrt{902}=2\sqrt{902}$$S_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{902}}{2*2}=\frac{60-2\sqrt{902}}{4} $$S_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{902}}{2*2}=\frac{60+2\sqrt{902}}{4} $
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