1/2y-y=50-70

Solution for 1/2y-y=50-70 equation:

1/2y-y=50-70

We move all terms to the left:

1/2y-y-(50-70)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

1/2y-y-(-20)=0

We add all the numbers together, and all the variables

-1y+1/2y+20=0

We multiply all the terms by the denominator


-1y*2y+20*2y+1=0

Wy multiply elements

-2y^2+40y+1=0

a = -2; b = 40; c = +1;
Δ = b2-4ac
Δ = 402-4·(-2)·1
Δ = 1608
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:

$\sqrt{\Delta}=\sqrt{1608}=\sqrt{4*402}=\sqrt{4}*\sqrt{402}=2\sqrt{402}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{402}}{2*-2}=\frac{-40-2\sqrt{402}}{-4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{402}}{2*-2}=\frac{-40+2\sqrt{402}}{-4}
$