/7y+1=3y+13

Solution for /7y+1=3y+13 equation:

/7y+1=3y+13

We move all terms to the left:

/7y+1-(3y+13)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We get rid of parentheses

/7y-3y-13+1=0

We multiply all the terms by the denominator


-3y*7y-13*7y+1*7y+=0

We add all the numbers together, and all the variables

-3y*7y-13*7y+1*7y=0

Wy multiply elements

-21y^2-91y+7y=0

We add all the numbers together, and all the variables

-21y^2-84y=0

a = -21; b = -84; c = 0;
Δ = b2-4ac
Δ = -842-4·(-21)·0
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-84}{2*-21}=\frac{0}{-42}
=0
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+84}{2*-21}=\frac{168}{-42}
=-4
$