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(4/7x)+(1/4x)=46
We move all terms to the left:
(4/7x)+(1/4x)-(46)=0
Domain of the equation: 7x)!=0
x!=0/1
x!=0
x∈R
Domain of the equation: 4x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
(+4/7x)+(+1/4x)-46=0
We get rid of parentheses
4/7x+1/4x-46=0
We calculate fractions
16x/28x^2+7x/28x^2-46=0
We multiply all the terms by the denominator
16x+7x-46*28x^2=0
We add all the numbers together, and all the variables
23x-46*28x^2=0
Wy multiply elements
-1288x^2+23x=0
a = -1288; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-1288)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{529}=23$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-1288}=\frac{-46}{-2576} =1/56 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-1288}=\frac{0}{-2576} =0 $
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