5/7y-3+3y=6

Solution for 5/7y-3+3y=6 equation:

5/7y-3+3y=6

We move all terms to the left:

5/7y-3+3y-(6)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R


We add all the numbers together, and all the variables

3y+5/7y-9=0

We multiply all the terms by the denominator


3y*7y-9*7y+5=0

Wy multiply elements

21y^2-63y+5=0

a = 21; b = -63; c = +5;
Δ = b2-4ac
Δ = -632-4·21·5
Δ = 3549
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:

$\sqrt{\Delta}=\sqrt{3549}=\sqrt{169*21}=\sqrt{169}*\sqrt{21}=13\sqrt{21}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-13\sqrt{21}}{2*21}=\frac{63-13\sqrt{21}}{42}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+13\sqrt{21}}{2*21}=\frac{63+13\sqrt{21}}{42}
$