/3y-7=8y+23

Solution for /3y-7=8y+23 equation:

/3y-7=8y+23

We move all terms to the left:

/3y-7-(8y+23)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We get rid of parentheses

/3y-8y-23-7=0

We multiply all the terms by the denominator


-8y*3y-23*3y-7*3y+=0

We add all the numbers together, and all the variables

-8y*3y-23*3y-7*3y=0

Wy multiply elements

-24y^2-69y-21y=0

We add all the numbers together, and all the variables

-24y^2-90y=0

a = -24; b = -90; c = 0;
Δ = b2-4ac
Δ = -902-4·(-24)·0
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-90}{2*-24}=\frac{0}{-48}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+90}{2*-24}=\frac{180}{-48}
=-3+3/4
$