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5/7x=6x
We move all terms to the left:
5/7x-(6x)=0
Domain of the equation: 7x!=0We add all the numbers together, and all the variables
x!=0/7
x!=0
x∈R
-6x+5/7x=0
We multiply all the terms by the denominator
-6x*7x+5=0
Wy multiply elements
-42x^2+5=0
a = -42; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-42)·5
Δ = 840
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{840}=\sqrt{4*210}=\sqrt{4}*\sqrt{210}=2\sqrt{210}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{210}}{2*-42}=\frac{0-2\sqrt{210}}{-84} =-\frac{2\sqrt{210}}{-84} =-\frac{\sqrt{210}}{-42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{210}}{2*-42}=\frac{0+2\sqrt{210}}{-84} =\frac{2\sqrt{210}}{-84} =\frac{\sqrt{210}}{-42} $
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