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3x+2/7x=12
We move all terms to the left:
3x+2/7x-(12)=0
Domain of the equation: 7x!=0We multiply all the terms by the denominator
x!=0/7
x!=0
x∈R
3x*7x-12*7x+2=0
Wy multiply elements
21x^2-84x+2=0
a = 21; b = -84; c = +2;
Δ = b2-4ac
Δ = -842-4·21·2
Δ = 6888
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6888}=\sqrt{4*1722}=\sqrt{4}*\sqrt{1722}=2\sqrt{1722}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1722}}{2*21}=\frac{84-2\sqrt{1722}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1722}}{2*21}=\frac{84+2\sqrt{1722}}{42} $
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