7/16y+6=8+38y

Solution for 7/16y+6=8+38y equation:

7/16y+6=8+38y

We move all terms to the left:

7/16y+6-(8+38y)=0


Domain of the equation: 16y!=0

y!=0/16

y!=0

y∈R


We add all the numbers together, and all the variables

7/16y-(38y+8)+6=0

We get rid of parentheses

7/16y-38y-8+6=0

We multiply all the terms by the denominator


-38y*16y-8*16y+6*16y+7=0

Wy multiply elements

-608y^2-128y+96y+7=0

We add all the numbers together, and all the variables

-608y^2-32y+7=0

a = -608; b = -32; c = +7;
Δ = b2-4ac
Δ = -322-4·(-608)·7
Δ = 18048
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:

$\sqrt{\Delta}=\sqrt{18048}=\sqrt{64*282}=\sqrt{64}*\sqrt{282}=8\sqrt{282}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{282}}{2*-608}=\frac{32-8\sqrt{282}}{-1216}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{282}}{2*-608}=\frac{32+8\sqrt{282}}{-1216}
$