1/2y+7=2y-2

Solution for 1/2y+7=2y-2 equation:

1/2y+7=2y-2

We move all terms to the left:

1/2y+7-(2y-2)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

1/2y-2y+2+7=0

We multiply all the terms by the denominator


-2y*2y+2*2y+7*2y+1=0

Wy multiply elements

-4y^2+4y+14y+1=0

We add all the numbers together, and all the variables

-4y^2+18y+1=0

a = -4; b = 18; c = +1;
Δ = b2-4ac
Δ = 182-4·(-4)·1
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{85}}{2*-4}=\frac{-18-2\sqrt{85}}{-8}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{85}}{2*-4}=\frac{-18+2\sqrt{85}}{-8}
$