2y+22/16y=190

Solution for 2y+22/16y=190 equation:

2y+22/16y=190

We move all terms to the left:

2y+22/16y-(190)=0


Domain of the equation: 16y!=0

y!=0/16

y!=0

y∈R


We multiply all the terms by the denominator


2y*16y-190*16y+22=0

Wy multiply elements

32y^2-3040y+22=0

a = 32; b = -3040; c = +22;
Δ = b2-4ac
Δ = -30402-4·32·22
Δ = 9238784
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:

$\sqrt{\Delta}=\sqrt{9238784}=\sqrt{256*36089}=\sqrt{256}*\sqrt{36089}=16\sqrt{36089}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3040)-16\sqrt{36089}}{2*32}=\frac{3040-16\sqrt{36089}}{64}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3040)+16\sqrt{36089}}{2*32}=\frac{3040+16\sqrt{36089}}{64}
$