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2y-(3y+4)/7y-(2-5y)=-9/58
We move all terms to the left:
2y-(3y+4)/7y-(2-5y)-(-9/58)=0
Domain of the equation: 7y!=0We add all the numbers together, and all the variables
y!=0/7
y!=0
y∈R
2y-(3y+4)/7y-(-5y+2)-(-9/58)=0
We get rid of parentheses
2y-(3y+4)/7y+5y-2+9/58=0
We calculate fractions
2y+5y+(-174y-232)/406y+63y/406y-2=0
We add all the numbers together, and all the variables
7y+(-174y-232)/406y+63y/406y-2=0
We multiply all the terms by the denominator
7y*406y+(-174y-232)+63y-2*406y=0
We add all the numbers together, and all the variables
63y+7y*406y+(-174y-232)-2*406y=0
Wy multiply elements
2842y^2+63y+(-174y-232)-812y=0
We get rid of parentheses
2842y^2+63y-174y-812y-232=0
We add all the numbers together, and all the variables
2842y^2-923y-232=0
a = 2842; b = -923; c = -232;
Δ = b2-4ac
Δ = -9232-4·2842·(-232)
Δ = 3489305
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}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-923)-\sqrt{3489305}}{2*2842}=\frac{923-\sqrt{3489305}}{5684} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-923)+\sqrt{3489305}}{2*2842}=\frac{923+\sqrt{3489305}}{5684} $
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