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

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

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

We move all terms to the left:

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


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

16y^2-4y-20y+3=0

We add all the numbers together, and all the variables

16y^2-24y+3=0

a = 16; b = -24; c = +3;
Δ = b2-4ac
Δ = -242-4·16·3
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{6}}{2*16}=\frac{24-8\sqrt{6}}{32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{6}}{2*16}=\frac{24+8\sqrt{6}}{32}
$