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6/7x-1/4x+10=11/4x
We move all terms to the left:
6/7x-1/4x+10-(11/4x)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 4x!=0
x!=0/4
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
6/7x-1/4x-(+11/4x)+10=0
We get rid of parentheses
6/7x-1/4x-11/4x+10=0
We calculate fractions
24x/28x^2+(-77x-1)/28x^2+10=0
We multiply all the terms by the denominator
24x+(-77x-1)+10*28x^2=0
Wy multiply elements
280x^2+24x+(-77x-1)=0
We get rid of parentheses
280x^2+24x-77x-1=0
We add all the numbers together, and all the variables
280x^2-53x-1=0
a = 280; b = -53; c = -1;
Δ = b2-4ac
Δ = -532-4·280·(-1)
Δ = 3929
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-\sqrt{3929}}{2*280}=\frac{53-\sqrt{3929}}{560} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+\sqrt{3929}}{2*280}=\frac{53+\sqrt{3929}}{560} $
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