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-1/7a-4=7/4a-3
We move all terms to the left:
-1/7a-4-(7/4a-3)=0
Domain of the equation: 7a!=0
a!=0/7
a!=0
a∈R
Domain of the equation: 4a-3)!=0We get rid of parentheses
a∈R
-1/7a-7/4a+3-4=0
We calculate fractions
(-4a)/28a^2+(-49a)/28a^2+3-4=0
We add all the numbers together, and all the variables
(-4a)/28a^2+(-49a)/28a^2-1=0
We multiply all the terms by the denominator
(-4a)+(-49a)-1*28a^2=0
Wy multiply elements
-28a^2+(-4a)+(-49a)=0
We get rid of parentheses
-28a^2-4a-49a=0
We add all the numbers together, and all the variables
-28a^2-53a=0
a = -28; b = -53; c = 0;
Δ = b2-4ac
Δ = -532-4·(-28)·0
Δ = 2809
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{2809}=53$$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-53}{2*-28}=\frac{0}{-56} =0 $$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+53}{2*-28}=\frac{106}{-56} =-1+25/28 $
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