22/8y+2y=190

Solution for 22/8y+2y=190 equation:

22/8y+2y=190

We move all terms to the left:

22/8y+2y-(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

2y+22/8y-190=0

We multiply all the terms by the denominator


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}
$