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-3/2a-7/5a=-29/30
We move all terms to the left:
-3/2a-7/5a-(-29/30)=0
Domain of the equation: 2a!=0
a!=0/2
a!=0
a∈R
Domain of the equation: 5a!=0We get rid of parentheses
a!=0/5
a!=0
a∈R
-3/2a-7/5a+29/30=0
We calculate fractions
1450a^2/900a^2+(-1350a)/900a^2+(-1260a)/900a^2=0
We multiply all the terms by the denominator
1450a^2+(-1350a)+(-1260a)=0
We get rid of parentheses
1450a^2-1350a-1260a=0
We add all the numbers together, and all the variables
1450a^2-2610a=0
a = 1450; b = -2610; c = 0;
Δ = b2-4ac
Δ = -26102-4·1450·0
Δ = 6812100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{6812100}=2610$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2610)-2610}{2*1450}=\frac{0}{2900} =0 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2610)+2610}{2*1450}=\frac{5220}{2900} =1+4/5 $
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