3/4y+5=4y-8

Solution for 3/4y+5=4y-8 equation:

3/4y+5=4y-8

We move all terms to the left:

3/4y+5-(4y-8)=0


Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We get rid of parentheses

3/4y-4y+8+5=0

We multiply all the terms by the denominator


-4y*4y+8*4y+5*4y+3=0

Wy multiply elements

-16y^2+32y+20y+3=0

We add all the numbers together, and all the variables

-16y^2+52y+3=0

a = -16; b = 52; c = +3;
Δ = b2-4ac
Δ = 522-4·(-16)·3
Δ = 2896
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:

$\sqrt{\Delta}=\sqrt{2896}=\sqrt{16*181}=\sqrt{16}*\sqrt{181}=4\sqrt{181}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{181}}{2*-16}=\frac{-52-4\sqrt{181}}{-32}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{181}}{2*-16}=\frac{-52+4\sqrt{181}}{-32}
$