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2-2s=11/4s+13
We move all terms to the left:
2-2s-(11/4s+13)=0
Domain of the equation: 4s+13)!=0We get rid of parentheses
s∈R
-2s-11/4s-13+2=0
We multiply all the terms by the denominator
-2s*4s-13*4s+2*4s-11=0
Wy multiply elements
-8s^2-52s+8s-11=0
We add all the numbers together, and all the variables
-8s^2-44s-11=0
a = -8; b = -44; c = -11;
Δ = b2-4ac
Δ = -442-4·(-8)·(-11)
Δ = 1584
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}$$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-12\sqrt{11}}{2*-8}=\frac{44-12\sqrt{11}}{-16} $$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+12\sqrt{11}}{2*-8}=\frac{44+12\sqrt{11}}{-16} $
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