0,25y+5=23-1/12y

Solution for 0,25y+5=23-1/12y equation:

0.25y+5=23-1/12y

We move all terms to the left:

0.25y+5-(23-1/12y)=0


Domain of the equation: 12y)!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

0.25y-(-1/12y+23)+5=0

We get rid of parentheses

0.25y+1/12y-23+5=0

We multiply all the terms by the denominator


(0.25y)*12y-23*12y+5*12y+1=0

We add all the numbers together, and all the variables

(+0.25y)*12y-23*12y+5*12y+1=0

We multiply parentheses

0y^2-23*12y+5*12y+1=0

Wy multiply elements

0y^2-276y+60y+1=0

We add all the numbers together, and all the variables

y^2-216y+1=0

a = 1; b = -216; c = +1;
Δ = b2-4ac
Δ = -2162-4·1·1
Δ = 46652
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:

$\sqrt{\Delta}=\sqrt{46652}=\sqrt{4*11663}=\sqrt{4}*\sqrt{11663}=2\sqrt{11663}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-216)-2\sqrt{11663}}{2*1}=\frac{216-2\sqrt{11663}}{2}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-216)+2\sqrt{11663}}{2*1}=\frac{216+2\sqrt{11663}}{2}
$