11/8(2y)+2y=190

Solution for 11/8(2y)+2y=190 equation:

11/8(2y)+2y=190

We move all terms to the left:

11/8(2y)+2y-(190)=0


Domain of the equation: 82y!=0

y!=0/82

y!=0

y∈R


We add all the numbers together, and all the variables

2y+11/82y-190=0

We multiply all the terms by the denominator


2y*82y-190*82y+11=0

Wy multiply elements

164y^2-15580y+11=0

a = 164; b = -15580; c = +11;
Δ = b2-4ac
Δ = -155802-4·164·11
Δ = 242729184
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:

$\sqrt{\Delta}=\sqrt{242729184}=\sqrt{16*15170574}=\sqrt{16}*\sqrt{15170574}=4\sqrt{15170574}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15580)-4\sqrt{15170574}}{2*164}=\frac{15580-4\sqrt{15170574}}{328}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15580)+4\sqrt{15170574}}{2*164}=\frac{15580+4\sqrt{15170574}}{328}
$