-6y+14/4y=32

Solution for -6y+14/4y=32 equation:

-6y+14/4y=32

We move all terms to the left:

-6y+14/4y-(32)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We multiply all the terms by the denominator


-6y*4y-32*4y+14=0

Wy multiply elements

-24y^2-128y+14=0

a = -24; b = -128; c = +14;
Δ = b2-4ac
Δ = -1282-4·(-24)·14
Δ = 17728
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:

$\sqrt{\Delta}=\sqrt{17728}=\sqrt{64*277}=\sqrt{64}*\sqrt{277}=8\sqrt{277}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-8\sqrt{277}}{2*-24}=\frac{128-8\sqrt{277}}{-48}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+8\sqrt{277}}{2*-24}=\frac{128+8\sqrt{277}}{-48}
$