5/36y+10=12y

Solution for 5/36y+10=12y equation:

5/36y+10=12y

We move all terms to the left:

5/36y+10-(12y)=0


Domain of the equation: 36y!=0

y!=0/36

y!=0

y∈R


We add all the numbers together, and all the variables

-12y+5/36y+10=0

We multiply all the terms by the denominator


-12y*36y+10*36y+5=0

Wy multiply elements

-432y^2+360y+5=0

a = -432; b = 360; c = +5;
Δ = b2-4ac
Δ = 3602-4·(-432)·5
Δ = 138240
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:

$\sqrt{\Delta}=\sqrt{138240}=\sqrt{9216*15}=\sqrt{9216}*\sqrt{15}=96\sqrt{15}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(360)-96\sqrt{15}}{2*-432}=\frac{-360-96\sqrt{15}}{-864}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(360)+96\sqrt{15}}{2*-432}=\frac{-360+96\sqrt{15}}{-864}
$