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2/5x+x=14
We move all terms to the left:
2/5x+x-(14)=0
Domain of the equation: 5x!=0We add all the numbers together, and all the variables
x!=0/5
x!=0
x∈R
x+2/5x-14=0
We multiply all the terms by the denominator
x*5x-14*5x+2=0
Wy multiply elements
5x^2-70x+2=0
a = 5; b = -70; c = +2;
Δ = b2-4ac
Δ = -702-4·5·2
Δ = 4860
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4860}=\sqrt{324*15}=\sqrt{324}*\sqrt{15}=18\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-18\sqrt{15}}{2*5}=\frac{70-18\sqrt{15}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+18\sqrt{15}}{2*5}=\frac{70+18\sqrt{15}}{10} $
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