190=22/8y+2y

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

190=22/8y+2y

We move all terms to the left:

190-(22/8y+2y)=0


Domain of the equation: 8y+2y)!=0

y∈R


We add all the numbers together, and all the variables

-(+2y+22/8y)+190=0

We get rid of parentheses

-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}
$