-1/2y+3=8y-14

Solution for -1/2y+3=8y-14 equation:

-1/2y+3=8y-14

We move all terms to the left:

-1/2y+3-(8y-14)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

-1/2y-8y+14+3=0

We multiply all the terms by the denominator


-8y*2y+14*2y+3*2y-1=0

Wy multiply elements

-16y^2+28y+6y-1=0

We add all the numbers together, and all the variables

-16y^2+34y-1=0

a = -16; b = 34; c = -1;
Δ = b2-4ac
Δ = 342-4·(-16)·(-1)
Δ = 1092
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:

$\sqrt{\Delta}=\sqrt{1092}=\sqrt{4*273}=\sqrt{4}*\sqrt{273}=2\sqrt{273}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{273}}{2*-16}=\frac{-34-2\sqrt{273}}{-32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{273}}{2*-16}=\frac{-34+2\sqrt{273}}{-32}
$