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x/6x-11=4x+13
We move all terms to the left:
x/6x-11-(4x+13)=0
Domain of the equation: 6x!=0We get rid of parentheses
x!=0/6
x!=0
x∈R
x/6x-4x-13-11=0
We multiply all the terms by the denominator
x-4x*6x-13*6x-11*6x=0
Wy multiply elements
-24x^2+x-78x-66x=0
We add all the numbers together, and all the variables
-24x^2-143x=0
a = -24; b = -143; c = 0;
Δ = b2-4ac
Δ = -1432-4·(-24)·0
Δ = 20449
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{20449}=143$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-143)-143}{2*-24}=\frac{0}{-48} =0 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-143)+143}{2*-24}=\frac{286}{-48} =-5+23/24 $
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