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x-11=6/7x+14
We move all terms to the left:
x-11-(6/7x+14)=0
Domain of the equation: 7x+14)!=0We get rid of parentheses
x∈R
x-6/7x-14-11=0
We multiply all the terms by the denominator
x*7x-14*7x-11*7x-6=0
Wy multiply elements
7x^2-98x-77x-6=0
We add all the numbers together, and all the variables
7x^2-175x-6=0
a = 7; b = -175; c = -6;
Δ = b2-4ac
Δ = -1752-4·7·(-6)
Δ = 30793
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{-(-175)-\sqrt{30793}}{2*7}=\frac{175-\sqrt{30793}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-175)+\sqrt{30793}}{2*7}=\frac{175+\sqrt{30793}}{14} $
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