3/4y-6=1/7y+4

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Solution for 3/4y-6=1/7y+4 equation:



3/4y-6=1/7y+4
We move all terms to the left:
3/4y-6-(1/7y+4)=0
Domain of the equation: 4y!=0
y!=0/4
y!=0
y∈R
Domain of the equation: 7y+4)!=0
y∈R
We get rid of parentheses
3/4y-1/7y-4-6=0
We calculate fractions
21y/28y^2+(-4y)/28y^2-4-6=0
We add all the numbers together, and all the variables
21y/28y^2+(-4y)/28y^2-10=0
We multiply all the terms by the denominator
21y+(-4y)-10*28y^2=0
Wy multiply elements
-280y^2+21y+(-4y)=0
We get rid of parentheses
-280y^2+21y-4y=0
We add all the numbers together, and all the variables
-280y^2+17y=0
a = -280; b = 17; c = 0;
Δ = b2-4ac
Δ = 172-4·(-280)·0
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-17}{2*-280}=\frac{-34}{-560} =17/280 $
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+17}{2*-280}=\frac{0}{-560} =0 $

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