6/8y-5y=-2

Solution for 6/8y-5y=-2 equation:

6/8y-5y=-2

We move all terms to the left:

6/8y-5y-(-2)=0


Domain of the equation: 8y!=0

y!=0/8

y!=0

y∈R


We add all the numbers together, and all the variables

-5y+6/8y+2=0

We multiply all the terms by the denominator


-5y*8y+2*8y+6=0

Wy multiply elements

-40y^2+16y+6=0

a = -40; b = 16; c = +6;
Δ = b2-4ac
Δ = 162-4·(-40)·6
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-8\sqrt{19}}{2*-40}=\frac{-16-8\sqrt{19}}{-80}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+8\sqrt{19}}{2*-40}=\frac{-16+8\sqrt{19}}{-80}
$