3y-4/5y+6=0

Solution for 3y-4/5y+6=0 equation:

3y-4/5y+6=0


Domain of the equation: 5y!=0

y!=0/5

y!=0

y∈R


We multiply all the terms by the denominator


3y*5y+6*5y-4=0

Wy multiply elements

15y^2+30y-4=0

a = 15; b = 30; c = -4;
Δ = b2-4ac
Δ = 302-4·15·(-4)
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-2\sqrt{285}}{2*15}=\frac{-30-2\sqrt{285}}{30}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+2\sqrt{285}}{2*15}=\frac{-30+2\sqrt{285}}{30}
$