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1/2s+3/4s+1/4s=+4
We move all terms to the left:
1/2s+3/4s+1/4s-(+4)=0
Domain of the equation: 2s!=0
s!=0/2
s!=0
s∈R
Domain of the equation: 4s!=0We add all the numbers together, and all the variables
s!=0/4
s!=0
s∈R
1/2s+3/4s+1/4s-4=0
We calculate fractions
4s/8s^2+(2s+3)/8s^2-4=0
We multiply all the terms by the denominator
4s+(2s+3)-4*8s^2=0
Wy multiply elements
-32s^2+4s+(2s+3)=0
We get rid of parentheses
-32s^2+4s+2s+3=0
We add all the numbers together, and all the variables
-32s^2+6s+3=0
a = -32; b = 6; c = +3;
Δ = b2-4ac
Δ = 62-4·(-32)·3
Δ = 420
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}$$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$$s_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{105}}{2*-32}=\frac{-6-2\sqrt{105}}{-64} $$s_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{105}}{2*-32}=\frac{-6+2\sqrt{105}}{-64} $
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