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11/8y+y+11/8y+y=190
We move all terms to the left:
11/8y+y+11/8y+y-(190)=0
Domain of the equation: 8y!=0We add all the numbers together, and all the variables
y!=0/8
y!=0
y∈R
2y+11/8y+11/8y-190=0
We multiply all the terms by the denominator
2y*8y-190*8y+11+11=0
We add all the numbers together, and all the variables
2y*8y-190*8y+22=0
Wy multiply elements
16y^2-1520y+22=0
a = 16; b = -1520; c = +22;
Δ = b2-4ac
Δ = -15202-4·16·22
Δ = 2308992
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2308992}=\sqrt{64*36078}=\sqrt{64}*\sqrt{36078}=8\sqrt{36078}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1520)-8\sqrt{36078}}{2*16}=\frac{1520-8\sqrt{36078}}{32} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1520)+8\sqrt{36078}}{2*16}=\frac{1520+8\sqrt{36078}}{32} $
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