5/6y-3/4y=10

Solution for 5/6y-3/4y=10 equation:

5/6y-3/4y=10

We move all terms to the left:

5/6y-3/4y-(10)=0


Domain of the equation: 6y!=0

y!=0/6

y!=0

y∈R



Domain of the equation: 4y!=0

y!=0/4

y!=0

y∈R


We calculate fractions


20y/24y^2+(-18y)/24y^2-10=0

We multiply all the terms by the denominator


20y+(-18y)-10*24y^2=0

Wy multiply elements

-240y^2+20y+(-18y)=0

We get rid of parentheses

-240y^2+20y-18y=0

We add all the numbers together, and all the variables

-240y^2+2y=0

a = -240; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·(-240)·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*-240}=\frac{-4}{-480}
=1/120
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*-240}=\frac{0}{-480}
=0
$