-6/7y+2+5/2y=-13/2

Solution for -6/7y+2+5/2y=-13/2 equation:

-6/7y+2+5/2y=-13/2

We move all terms to the left:

-6/7y+2+5/2y-(-13/2)=0


Domain of the equation: 7y!=0

y!=0/7

y!=0

y∈R



Domain of the equation: 2y!=0

y!=0/2

y!=0

y∈R


We get rid of parentheses

-6/7y+5/2y+2+13/2=0

We calculate fractions


(-48y)/56y^2+35y/56y^2+91y/56y^2+2=0

We multiply all the terms by the denominator


(-48y)+35y+91y+2*56y^2=0

We add all the numbers together, and all the variables

126y+(-48y)+2*56y^2=0

Wy multiply elements

112y^2+126y+(-48y)=0

We get rid of parentheses

112y^2+126y-48y=0

We add all the numbers together, and all the variables

112y^2+78y=0

a = 112; b = 78; c = 0;
Δ = b2-4ac
Δ = 782-4·112·0
Δ = 6084
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6084}=78$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(78)-78}{2*112}=\frac{-156}{224}
=-39/56
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(78)+78}{2*112}=\frac{0}{224}
=0
$