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-2s=3/4s+13
We move all terms to the left:
-2s-(3/4s+13)=0
Domain of the equation: 4s+13)!=0We get rid of parentheses
s∈R
-2s-3/4s-13=0
We multiply all the terms by the denominator
-2s*4s-13*4s-3=0
Wy multiply elements
-8s^2-52s-3=0
a = -8; b = -52; c = -3;
Δ = b2-4ac
Δ = -522-4·(-8)·(-3)
Δ = 2608
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}$$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2608}=\sqrt{16*163}=\sqrt{16}*\sqrt{163}=4\sqrt{163}$$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-4\sqrt{163}}{2*-8}=\frac{52-4\sqrt{163}}{-16} $$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+4\sqrt{163}}{2*-8}=\frac{52+4\sqrt{163}}{-16} $
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