4y+1/3y-5=0

Solution for 4y+1/3y-5=0 equation:

4y+1/3y-5=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We multiply all the terms by the denominator


4y*3y-5*3y+1=0

Wy multiply elements

12y^2-15y+1=0

a = 12; b = -15; c = +1;
Δ = b2-4ac
Δ = -152-4·12·1
Δ = 177
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-\sqrt{177}}{2*12}=\frac{15-\sqrt{177}}{24}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{177}}{2*12}=\frac{15+\sqrt{177}}{24}
$