190=y+11/8y

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

190=y+11/8y

We move all terms to the left:

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


Domain of the equation: 8y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-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}
$