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2/7x+2x-5=6x
We move all terms to the left:
2/7x+2x-5-(6x)=0
Domain of the equation: 7x!=0We add all the numbers together, and all the variables
x!=0/7
x!=0
x∈R
-4x+2/7x-5=0
We multiply all the terms by the denominator
-4x*7x-5*7x+2=0
Wy multiply elements
-28x^2-35x+2=0
a = -28; b = -35; c = +2;
Δ = b2-4ac
Δ = -352-4·(-28)·2
Δ = 1449
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-3\sqrt{161}}{2*-28}=\frac{35-3\sqrt{161}}{-56} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+3\sqrt{161}}{2*-28}=\frac{35+3\sqrt{161}}{-56} $
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