6(8/7y+4)=4(5/2y-5)

Solution for 6(8/7y+4)=4(5/2y-5) equation:

6(8/7y+4)=4(5/2y-5)

We move all terms to the left:

6(8/7y+4)-(4(5/2y-5))=0


Domain of the equation: 7y+4)!=0

y∈R



Domain of the equation: 2y-5))!=0

y∈R


We multiply parentheses

48y-(4(5/2y-5))+24=0

We multiply all the terms by the denominator


48y*2y+24*2y-5))-(4(5-5))=0

We add all the numbers together, and all the variables

48y*2y+24*2y-5))-(40)=0

We add all the numbers together, and all the variables

48y*2y+24*2y=0

Wy multiply elements

96y^2+48y=0

a = 96; b = 48; c = 0;
Δ = b2-4ac
Δ = 482-4·96·0
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-48}{2*96}=\frac{-96}{192}
=-1/2
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+48}{2*96}=\frac{0}{192}
=0
$