1/2y+y-4=31

Solution for 1/2y+y-4=31 equation:

1/2y+y-4=31

We move all terms to the left:

1/2y+y-4-(31)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

y+1/2y-35=0

We multiply all the terms by the denominator


y*2y-35*2y+1=0

Wy multiply elements

2y^2-70y+1=0

a = 2; b = -70; c = +1;
Δ = b2-4ac
Δ = -702-4·2·1
Δ = 4892
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:

$\sqrt{\Delta}=\sqrt{4892}=\sqrt{4*1223}=\sqrt{4}*\sqrt{1223}=2\sqrt{1223}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1223}}{2*2}=\frac{70-2\sqrt{1223}}{4}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1223}}{2*2}=\frac{70+2\sqrt{1223}}{4}
$