1/2y+3.5y=20

Solution for 1/2y+3.5y=20 equation:

1/2y+3.5y=20

We move all terms to the left:

1/2y+3.5y-(20)=0


Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We add all the numbers together, and all the variables

3.5y+1/2y-20=0

We multiply all the terms by the denominator


(3.5y)*2y-20*2y+1=0

We add all the numbers together, and all the variables

(+3.5y)*2y-20*2y+1=0

We multiply parentheses

6y^2-20*2y+1=0

Wy multiply elements

6y^2-40y+1=0

a = 6; b = -40; c = +1;
Δ = b2-4ac
Δ = -402-4·6·1
Δ = 1576
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:

$\sqrt{\Delta}=\sqrt{1576}=\sqrt{4*394}=\sqrt{4}*\sqrt{394}=2\sqrt{394}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{394}}{2*6}=\frac{40-2\sqrt{394}}{12}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{394}}{2*6}=\frac{40+2\sqrt{394}}{12}
$