1/4y-5=-3y+6

Solution for 1/4y-5=-3y+6 equation:

1/4y-5=-3y+6

We move all terms to the left:

1/4y-5-(-3y+6)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

1/4y+3y-6-5=0

We multiply all the terms by the denominator


3y*4y-6*4y-5*4y+1=0

Wy multiply elements

12y^2-24y-20y+1=0

We add all the numbers together, and all the variables

12y^2-44y+1=0

a = 12; b = -44; c = +1;
Δ = b2-4ac
Δ = -442-4·12·1
Δ = 1888
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:

$\sqrt{\Delta}=\sqrt{1888}=\sqrt{16*118}=\sqrt{16}*\sqrt{118}=4\sqrt{118}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{118}}{2*12}=\frac{44-4\sqrt{118}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{118}}{2*12}=\frac{44+4\sqrt{118}}{24}
$