11/8y+y=190

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Solution for 11/8y+y=190 equation: 



11/8y+y=190

We move all terms to the left:

11/8y+y-(190)=0



Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R



We add all the numbers together, and all the variables

y+11/8y-190=0

We multiply all the terms by the denominator


y*8y-190*8y+11=0

Wy multiply elements

8y^2-1520y+11=0

a = 8; b = -1520; c = +11;
Δ = b2-4ac
Δ = -15202-4·8·11
Δ = 2310048
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:


$\sqrt{\Delta}=\sqrt{2310048}=\sqrt{144*16042}=\sqrt{144}*\sqrt{16042}=12\sqrt{16042}$


$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1520)-12\sqrt{16042}}{2*8}=\frac{1520-12\sqrt{16042}}{16}
$


$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1520)+12\sqrt{16042}}{2*8}=\frac{1520+12\sqrt{16042}}{16}
$

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