(2/7)y-5/6+(5/7)y=7/6

Solution for (2/7)y-5/6+(5/7)y=7/6 equation:

(2/7)y-5/6+(5/7)y=7/6

We move all terms to the left:

(2/7)y-5/6+(5/7)y-(7/6)=0


Domain of the equation: 7)y!=0

y!=0/1

y!=0

y∈R


We add all the numbers together, and all the variables

(+2/7)y+(+5/7)y-5/6-(+7/6)=0

We multiply parentheses

2y^2+5y^2-5/6-(+7/6)=0

We get rid of parentheses

2y^2+5y^2-5/6-7/6=0

We multiply all the terms by the denominator


2y^2*6+5y^2*6-5-7=0

We add all the numbers together, and all the variables

2y^2*6+5y^2*6-12=0

Wy multiply elements

12y^2+30y^2-12=0

We add all the numbers together, and all the variables

42y^2-12=0

a = 42; b = 0; c = -12;
Δ = b2-4ac
Δ = 02-4·42·(-12)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{14}}{2*42}=\frac{0-12\sqrt{14}}{84}
=-\frac{12\sqrt{14}}{84}
=-\frac{\sqrt{14}}{7}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{14}}{2*42}=\frac{0+12\sqrt{14}}{84}
=\frac{12\sqrt{14}}{84}
=\frac{\sqrt{14}}{7}
$