2y+11/8*2y=190

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

2y+11/8*2y=190

We move all terms to the left:

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


Domain of the equation: 8*2y!=0

y!=0/1

y!=0

y∈R


We multiply all the terms by the denominator


2y*8*2y-190*8*2y+11=0

Wy multiply elements

32y^2*2-3040y*2+11=0

Wy multiply elements

64y^2-6080y+11=0

a = 64; b = -6080; c = +11;
Δ = b2-4ac
Δ = -60802-4·64·11
Δ = 36963584
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:

$\sqrt{\Delta}=\sqrt{36963584}=\sqrt{256*144389}=\sqrt{256}*\sqrt{144389}=16\sqrt{144389}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6080)-16\sqrt{144389}}{2*64}=\frac{6080-16\sqrt{144389}}{128}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6080)+16\sqrt{144389}}{2*64}=\frac{6080+16\sqrt{144389}}{128}
$