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1/5x+7x=12
We move all terms to the left:
1/5x+7x-(12)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
7x+1/5x-12=0
We multiply all the terms by the denominator
7x*5x-12*5x+1=0
Wy multiply elements
35x^2-60x+1=0
a = 35; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·35·1
Δ = 3460
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3460}=\sqrt{4*865}=\sqrt{4}*\sqrt{865}=2\sqrt{865}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{865}}{2*35}=\frac{60-2\sqrt{865}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{865}}{2*35}=\frac{60+2\sqrt{865}}{70} $
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