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1/3x+7x=154
We move all terms to the left:
1/3x+7x-(154)=0
Domain of the equation: 3x!=0We add all the numbers together, and all the variables
x!=0/3
x!=0
x∈R
7x+1/3x-154=0
We multiply all the terms by the denominator
7x*3x-154*3x+1=0
Wy multiply elements
21x^2-462x+1=0
a = 21; b = -462; c = +1;
Δ = b2-4ac
Δ = -4622-4·21·1
Δ = 213360
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{213360}=\sqrt{16*13335}=\sqrt{16}*\sqrt{13335}=4\sqrt{13335}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-462)-4\sqrt{13335}}{2*21}=\frac{462-4\sqrt{13335}}{42} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-462)+4\sqrt{13335}}{2*21}=\frac{462+4\sqrt{13335}}{42} $
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